Short version - Read me first

If all that you need is instructions on what to buy, here's the short version:

The Drumkit: Anything from here, or here that is over $600CAN and less than $1000CAN after taxes. Look for things with "hardware included", avoid "shell packs" or "shells only".
The Sticks: Vic Firth 5A
Reduce volume with: Drum Mutes - any brand will do as long as you have a mute for each drum and cymbal

For specifics, keep reading the other topics below

General Advice

• Cheap gear is bad: Poorly manufactured drumsets become garbage very quickly, and generally need more replacing and work than well-made kits. They also generally feel bad to play - and little is more frustrating than having a 300$ purchase go to waste because a student just doesn't like playing it and doesn't know why. My goal is to help you purchase a kit once, and not have to do so again until you're in a recording studio!
• Bargains are good: The prices I list in here are the average retail prices. If you can manage to find the same items at a fraction of the price: go for it! It is not the price that is important, but the quality! Community sites and pages like Kijiji or Ebay are fantastic for finding great deals.
• Research before you buy: Avoid brands with little online or community presense. My own first kit was a 100$ kit sold to my parents for 400$ (marked down from the 600$ price tag, of course!) with a fake brand name spray-painted on the front. Months later, well after the kit started breaking, the same type of kit was on sale for 400$ with a completely different made-up brand name. While this isn't common, a simple Google search could have saved us a lot of trouble up front. I recommend looking up as much as you can on Youtube - where you can see/hear the instruments yourself and check the comments.
• Upgrades (after a while) are likely: The cymbals, drumheads, and hardware that come with most beginner kits are rarely kept forever and are usually upgraded to their "final" versions later on. As such, expect your beginner gear to show signs of wear at some point within the first year; by the time this happens, you'll likely be better aware of what you should purchase to replace them. And don't worry: your SECOND cymbals, heads, and hardware last much longer than the first.
• Throw a towel into your bass drum: Yes, really. If your bass drum sounds "boingy" or ringy, open it up and push an old towel up to the batter head. It will give your sound more "punch" and make it sound more like the kicks you hear in rock or hiphop.

Should I choose an electric kit or an acoustic kit?

There are two basic choices for home drumsets. Both electric drumsets and acoustic drumsets are completely valid choices for beginners looking to learn drumkit. While both have their ups and downs, exactly what you need will depend on your particular circumstances.

Acoustic Drums are a must-have for any student looking to become serious in their training. The main benefit of acoustic drums is that they are the real deal: no compromises have to be made for technique, the touch developped on the instrument is transferable to almost any other instrument, and they tend to age very well (a drumset purchsed in the 50s is just as valid as a drumkit purchased today). My personal recommendation is an acoustic set.

Pros

• Authentic: Developing touch and control on a drum kit allows for proficiency across a variety of instruments including most mallet instruments and world percussion. Playing on a real kit also offers the versatility and creative control of a real instrument and will always respond better than a triggered imitation.
• Upgradeable: Cymbals, drum heads, and careful tuning can turn even the most basic of starter drumkits into a fantastic sounding instrument. The initial investment into an acoustic drumkit is rarely wasted, as in the right hands, they can sound fantastic well into the late-intermiediate level.
• Industry Standard: Every venue, recording studio, and rehearsal hall that I have encountered uses acoustic drums - e-kits are simply not needed in these situations as more often than not the sounds that they offer can more easily be programmed than played. Being familiar with acoustic kits and knowing how to draw sounds from these kits is absolutely essential when doing any drumming with other musicians.

Cons

• Loud: Acoustic kits are powerful instruments, and beginners (who lack touch and control) may find it hard to control their volume. This can be mitigated with mutes or mesh heads, but those come at an extra cost.
• Bulky: While e-kits are only marginally smaller than acoustic kits while set up (by a matter of only a foot or two in most cases), acoustic kits take up much more general space when being stored. The shells are generally stacked and hardware, cymbals, and pedals must be stored as well.
• Inability to change inherent sounds: Acoustic drums simply cannot reproduce the sounds of sampled sub-bass, fingersnaps, or reverse cymbals heard in many modern EDM styles. E-kits have access to most of the sounds available to acoustic kits, the same cannot be said for the latter.

Electric Drums are a fantastic tool for casual players or those looking for great practice tools. The main benefit to electric drums is that they have the benefit of electronic tools: metronomes, sound banks, and aux inputs are standard. The ability to record MIDI is great for any modern musician, and the consistent sounds of an electric kit guarantees full and clear performances. While I believe that acoustic kits are a better overall first purchase, electric kits are fantastic practice tools that can lead you very well into the late-intermiediate stages of learning.

Pros

• Huge toolbox: My own e-kit has playalong tracks, a metronome, timing games, sample imports, the ability to add pads... electronic kits have ALL the tools you need for variety in practice.
• Theoretically limitless sounds: With the ability to import sounds and bring in your own samples to the e-kit's "brain", you have essentially limitless potential when it comes to what sounds you have access to. This can be used to update your kit as old sounds go "out of style", or even create strange or unique sounds that are only yours.
• Quiet: Electronic drumkits are about as quiet as can be, which is a huge benefit for those living with neighbours or family. With the ability to put on headphones, or adjust your volume with a simple knob, there is never a need to compromise your playing for fear of noise.

Cons

• Not the real thing: Because Electric Kits rely on samples for their sounds, every hit sounds the same regardless of how it was played. This means that many e-kit players tend to be surprised with a poor, uncontrolled sound when they finally switch to an acoustic set later on. Acoustic hand-drum players can get dozens of sounds out of a single drum. Electronic pads generally max out at two.
• Expensive: I've found that simple electric kits that are worth playing, have long lives, and aren't flimsy and fragile, are generally in the 1000$+ range. By comparisson, a similarly priced acoustic kit may get you a professional sounding small set - far more bang for your buck. While there are e-kits for under 800$... I've yet to find one that did not loosen up, sound poor, or remain functional for any long period of time.
• Poor long-term investment: Technology advances quickly, and the legendary Roland 808 - one of the most used and popular drum machines of all time - is now available as a free app for my phone. Very few electronic drumkits maintain their value long-term, as with every generation, more and more features make the previous version obsolete.

How should I shop for drums?

When possible, I'd advise shopping second-hand or checking out used-markets like kijiji or ebay. People are upgrading every day and many are willing to part with their old gear for a fraction of its retail value. However, be sure to do your homework and compare the prices on offer with sites like Musician's Friend or your local music store. Also, while Amazon and other general retailers should be fine for things like sticks or accessories, avoid big-box stores for the instruments themselves.

A typical drumkit will have a kick/bass drum (the big drum on the bottom), a snare drum (a metal or wood drum with metal wires on the underside), one or two rack toms (simple drums that are mounted to the bass drum), a floor tom (similar to the rack toms, but with legs that are placed on the ground), a hihat (two cymbals linked together with a pedal), and a cymbal (usually a larger 20" ride cymbal, but many beginner kits come with an all-purpose generic 14-18" cymbal).

Some beginner kits come with one rack tom, some come with two. Many kits come with more, but any more than 2 won't be necessary. An average drum kit will have 4 cymbals (two hihats, a large 20" ride, and a medium 14"-18" sized crash), and many beginner kits combine the ride/crash into a generic cymbal. While most professional drummers have far more cymbals than this, beginners do not need more than these three basic cymbals.

Overall, the drumkit should look like this, or this, or this. You DO NOT want a kit that looks like this (this is a toy: notice there's no hihat, no floor tom - be wary of any drumkit with a cymbal stand built into the kick drum), or this (this is a Latin percussion kit - it's all professional gear, but contains none of the instruments found on a typical drumset), or this (this is a RockBand video game drumset - as crazy as it sounds, please make sure your drums actually make sounds before you purchase them).

When shopping, avoid anything with the word "Junior" (these are typically kids' play sets... they're generally not made well, aren't compatible with better gear, and are bad long-term investments), avoid "Shell packs" or "Shells only" (these are kits for professionals who are only looking for the drums themselves - no pedals, no hardware, only the bare minimum), and be wary of anything that retails for under 300$ - usually that's a sign that it's made of cheap materials that are likely to break after a few months of use.

Do you have examples of what to look for?

For a beginner, I would say that acoustic drums in the 500-900$ range will give you the best return on investment. For electronic drums, I would recommend most things in the 900-1500$ range.

At time of writing (August 2022), the Pearl Roadshow retails at roughly $600CAN and includes all hardware/cymbals needed to start playing immediately. Sonor, Gretsch, Pearl, Ludwig, Yamaha, Tama, and Mapex are the big companies to look out for when shopping for drums.

Many beginner kits come with factory cymbals, but these are intended to be replaced over time. As far as cymbals go, you'll want to pick up hihats, a ride cymbal, and a crash cymbal. Many cymbal companies provide packs that include all of these (and the occasional second crash). Presently Sabian and Zildjian offer the best beginner cymbal packs for the price.

As far as electronic kits go, Alesis has a mesh-head kit that retails for under $800CAN. This is about as low as I'd venture price-wise for electronic kits, and only because mesh-heads are the best for reducing sound. At this range you run into shakey kits, sub-par samples, and breakable pads. A better long-term investment may be the Roland TD17 series drum kit, which will run you around $1200CAN, but also has a myriad of build-in tools, has future-proofing upgrade packs available, and is generally a fantastic machine. Roland, Yamaha, Alesis are the big names in this category, and are the only ones I'd trust.

In terms of accessories, Vic Firth and Promark are the biggest names in drumsticks right now. Headhunters (a local Toronto company) also makes quality products along with some interesting "creations" (more on those later).

Drumsticks are classified by size using a number and letter. The lower the number (between 1-9), the wider the stick. The lower the letter, the denser the stick (between A-C). 7A sticks are small, thin, jazzy sticks. Whereas 2B sticks are heavy, thick sticks for Rock or Metal. Generally speaking, 5A drumsticks are average, "normal" drumsticks, but I encourage new students (especially younger ones) to choose whichever sticks they like the most. Avoid "kids" sticks - adult sizes won't hurt their technique in any meaningful way, and these small sticks don't have much use when they're outgrown.
Drumsticks should not run you more than $25CAN.

Mutes for acoustic drumkits are available, which reduce the total volume of kits dramatically. Here is a demo - the volume is comparable to striking a couch. Mesh Heads are also handy tools that replace the batter head (the drum head you hit) on your drums, reducing the volume GREATLY while also maintaining the tone of the drums. Here is a demo. For the cymbals, mute packs for acoustic drumsets should include cymbal mutes as well. However, low-volume cymbals do exist for practicing purposes. I would generally not recommend them for first drumkits (they're the most expensive option for sound reduction), but if you are sure that the kit will not be used for performances, they are easily the best option for reducing cymbal volume while maintaining tone and a realistic feel (and may be used later for stacks or triggering). Here is a demo.

Drum thrones and drum pedals come in a variety of styles and uses. Most beginner kits should come with pedals and throne in-box. If for whatever reason yours does not, you almost never be spending more than 200$CAN on both of these combined. Though both pedals and thrones have high-end models can range over $1000CAN, the lowest-end models of these will more than suffice. Avoid replacing a throne with a normal chair - this causes early back problems and hurts posture.

Drumkits are also immensely versatile and so drummers are VERY easy to purchase little gifts for. Moongel, Drum Honey, or even sticky hands can dramatically and instantly improve the sound of acoustic kits. Brushes, mallets, or rods/splatsticks are game-changers as well, and are loads of fun to play with. Drums are also fantastically customizable, so adding small percussion like tambourines, shakers, or cowbells are wonderful additions. NONE OF THESE ARE ESSENTIAL FOR FIRST-TIME PLAYERS, but make for fantastic gifts on holidays and birthdays.

What are the differences between a cheap kit and a good kit?

The most noticeable difference between low-cost cheap kits and their more well-made counterparts is their general flimsiness; the shells feel pliable, the heads are thin plastic, the metal rims are weak. What this generally results in is a drumkit that does not stay in tune. Your sound will generally become weaker between practice sessions (or even between songs, depending how hard you hit) and as the lugs loosen, they will release their hold on the drum heads, causing them to lose their tension and dent (making them essentially un-tunable for future sessions).
In addition, cheap kits break easily. Remember that drumkits are made to be hit; no part of it should crack, dent, or loosen through normal use. Cymbal stands on cheaper kits have a tendancy to loosen over time and occasionally fail, resulting in cracked cymbals.
Speaking of cymbals, unless your cymbals are specifically marked as "thin", they should not be easy to bend ("should not bend" applies to most items on your set). While typically, many beginner kits are equipped with cheap flexible cymbals for starting sets, cymbals are generally the first thing to be upgraded when investing in new equipment.

Oh no! My X broke! What do I do?!

The good news is, it's probably fine.

Drumsticks are the most common thing to break. Depending on how hard you hit and how thick your sticks are, drumsticks will generally break once every few months. My own sticks last about 2-4 months while playing on an acoustic kit for roughly two hours each day. If your drumsticks are breaking on a near-weekly basis, the problem is likely your technique. If you're the type of person who prides themselves on breaking drumsticks, consider the following chart:

• Are you the one buying your drumsticks?
  YES: Carry on.
  NO: Stop it.

The next most common thing to break are drum skins or heads, however this should be a fairly rare occurance (less than once per year). Drum skins should be replaced once every 6 months or so if you're playing professionally. For students, or hobbiests, I would say once a year is fine. If heads are left on for multiple years, they become weaker and weaker, until eventually they break. Drum heads that are too tight are generally the culprit in these situations, but having heads loose enough to dent will also result in their tearing. Skins are repleaceable but if you're having a problem with heads frequently breaking, consider re-evaluating your tuning techniques or switching to lighter sticks.

Electronics, or electric kit pads will occasionally break over time, especially through heavy use. Unfortunately, when this happens it's usually a dead trigger which is very hard to fix yourself. Fortunately, most of the big companies do offer individual parts for replacement and you can generally order in a new pad if you know what your brain (the computer that controls your electronic kit) is compatible with. The biggest danger here is discontinued parts, but fortunately many brains are compatible with a variety of triggers.

Stands and hardware can generally last for years, if properly maintained. However, over-tightening gear (which drummers are particularly guilty of) will reduce the lifespan of your stands. Loose or shaky stands can sometimes be repaired by simply tightening up the right screw, but generally it means having to buy a new stand. Yamaha stands are pricey, but well made: they're the only cymbal stand manufacturer I know that also make motorcycles!

Cymbals should very rarely break. It is possible to have the same cymbals your entire life without needing to replace them. The average life of a cymbal should be decades. If you are breaking cymbals more frequently than that, consider re-evaluating your technique, purchasing thicker cymbals, or using thinner sticks. If your cymbal is cracked, you can sometimes stop the crack from spreading by drilling a hole directly at the end of the crack, or cutting it out completely. If your cymbal is cracked beyond repair, you can always consider using it in a stack or as an effect, though its days as a normal cymbal are likely over.

Drum shells should never break through normal use. A drum shell that breaks is generally a sign of poor building materials or a LOT of abuse. The most common damage I've seen on drum shells are broken or loose lugs due to mistreatment or poor manufacturing. These can generally be fixed by simply screwing them back in (and maybe applying a small amount of wood glue just in case - though I would be VERY hesitant to try this with tuning lugs), but if the lugs broke free through normal playing... it may be time to pack up the kit and upgrade. The last time I had lugs that were that bad, I used the drum for the Icebucket Challenge.