Okay, to start off, there's no "good" or "bad" drumset. No matter how good you think your set is, there's always one better. The same thing goes for bad sets. It's what you do with the one you have and how you make it sound that counts. Yes, you'll be tuning your own kit. We'll get to that later.
Drumsets that will give you the richest sounds are going to be made from a woods like maple and cherry -maple being my preference, so I'll use it as the example more often. Cheap, $500 beginner shells (wooden part of a drum) are going to be made literally from plywood. A set made from maple is going to be easier to get that perfect sound from while you tune than a plywood set will, simply because the plywood set doesn't have the insulation and resonance that maple does -BUT... one can make a plywood set sound decent -even close enough to maple that anyone short of a professional won't be able to tell the difference- given proper tuning skills and experience. The shape is always round 😉 I'm going to assume that you understand that snares are made from either wood or some sort of metal -most of the time, aluminum. I'm going to get semi-deep into tuning, because that is ultimately what is going to make your drumset sound like a drumset. I'm also going to assume that you know that tuning a snare is a bit different than tuning a regular drum head, and I'm not going to get into it.
For a "five-piece," you'll get bass, snare, two toms, and a floor tom. That's the standard rock set. A standard jazz set has the lower of the two toms removed -and thus a four-piece. Most hard rock kits are either nine- or eleven-piece. Note: when counting drum kit "pieces," you don't include the cymbals, high-hats, and various other percussion parts/combinations like wood blocks or china splash (6" china laying with no buffer on top of a 6" splash as one cymbal. Try it some time; they sound PERFECT in the right setting).
Tuning can be easily more important than what materials that the drumset is made out of. I'm going to assume that you know nothing about tuning. When you get your set, you'll want to keep it in a place where the temperature doesn't fluxuate more than 20 degrees on a regular basis. The plastics will expand and contract and you'll end up tuning your drumset every two weeks - which can easily become a pain in the ass.
If you look at the top head of the drum that you wish to tune, you'll notice that for every lug (screw) holding the head down, there is one directly across from it. Drums always have an even number of lugs. The way you tune your set doesn't matter which lug you start with, because unless you're doing fine tuning at the last minute before a show or something, you always take both the top and bottom head (provided that there is one) off the drum and begin from scratch. When you take the head off, be sure to rotate the head atleast one lug around to make sure that if the shell has some sort of irregularity along the edge, that it won't damage the head out of shape too soon before you get your next paycheck to either get the shell fixed, replaced, or the head replaced. This doesn't happen often (because you LOOK for these things before you put the head on), but it does happen. When you fix the head back onto the shell, tighten all the lugs finger tight before you start yankin' down on the lugs with the drum key. As I said before, it doesn't matter which lug you start with, but fairly common practice is to start with that same lug (forcing you into a habbit) each time. Wherever you begin, turn the drumkey down on the lug only one revolution at a time. Then go to the lug on the opposite side of the head and do the same single full turn. When you've done that, go back to your original lug and go one lug left or right. Tighten it down one revolution, then do the one across from it as well. Then come back to it and go one lug right or left (the same direction you went previously) and continue for no more than three revolutions.
This is where it gets tricky. If you buy Remo Pinstripe brand heads, it's easier because of the pinstripe. But if you put your finger in the dead center of the head to deaden the sound, you should be able to hit the head gently at one lug (on the pinstripe in front of it), then hit the lug on the opposite side of the head and hear the same exact tone on it. Most people, not having perfect pitch, can't tell if it's off a little or not. Use your best judgement. Do this, going around the drum tuning opposite sides, in the same direction that you went around previously while turning one full circle with the drumkey. If the sounds don't match, put the drum key on one lug and twist it a quarter of a revolution or so, then hit the lugs again and adjust accordingly. Don't forget to tighten both lugs if necessary, but these can be done out of order because all you're looking for is a matching tone between these two lugs.
When you've got that drum tuned, you should be able to go around to each lug, in order along the outside (not just across from eachother), and hear the same exact tone on each one. If you have to turn more than 3.5 times tighter than the original finger-tightness, odds are that you've got it too tight. Time to pull it off and start again. But, if you succeed, it's on to the bottom head. This head should NOT be as tight as the top head. That way the top head vibrates at a higher frequency than the lower head and as the sound moves down the air and shell of the drum to the lower head as you hit it (imagine the sound moving in slow motion), the bottom head will begin to vibrate but at a lower frequency and give you a tone that seems to drop off lower instead of just a "thud" at a certain tone when you hit the tom. When you're playing, you'll notice a BIG difference between a "thud" and a dropping tone. This is the KEY to the better sounding sets out there.
When tuning a drumset, you might get your drums to "ring" a little, which is fine. You want that. When you're playing and the rest of the band is playing, you won't hear it very much at all (unless they're ringing too much, in which you'll want to re-tune the set or fine-tune it if you don't have time to start from scratch). It gives the set personality... feel... better fits into the groove when it sounds natural. DRUM DAMPENERS ARE EVIL -do not get into the habbit of using these because they will make you lazy and get you acustomed to hearing what a drumset should NOT sound like. The whole point to a drumset is to MAKE NOISE. Any good drummer will be able to tune his set and make sound good without having to kill some of the sound of it just to keep quiet. Another reason dampeners are used is to get rid of the ringing sound; again, if you know what you're doing, you can get the ring to go away if it's too loud, but a little ring is good. A good drummer will either be able to tune his set correctly or play with correct dynamics if he needs to play quieter -but where's the fun in that? 😉
And that concludes Lesson Number One.
nik