Buying drum heads:
The weight and thickness of the drum head largely decides the sound potential. Thin and light heads have a clear, resonating sound. Thicker, heavier heads have less resonance and shorter decay, but unfortunately also less tone. However, they are more durable. Coated heads have a different sound characteristic, as the coating enhances some of the overtones, and the resonance gets slightly shorter.
For an open, resonating sound, buy thin to medium, single ply drumheads - for a warmer, heavier sound buy thicker, double ply drum heads. Internal dampening rings muffle the overtones, leaving a clear and focused center tone. They especially work well on bass drums, but, in my opinion, they’re unnecessary on the other drums. Some people like to add an external dampening ring on the snare drum. Bottom (or resonance) heads on toms are almost always thin to medium weight, single ply heads.
Beware that snare side heads on snare drums require special heads.
Balancing the drum head:
Balancing the drum head means to make sure, once the head is mounted, that it has the same pitch all the way around the edge of the drum. You can check this by tapping the head lightly near each tuning rod. Adjust until they all play at the same pitch. This procedure guarantees you the maximum resonance from the drum head. It’s the same no matter the type or size of the drum.
Top and bottom drum heads:
Most drums have both top and bottom heads. These can be tuned to different or equal pitches as desired. One general rule applies when doing this: The head that is tuned to the higher pitch carries the most overtones, while the one that is tuned to the lower pitch carries more low resonance and center tone. So by choosing the relation between top and bottom head you can decide the sound characteristic of your drum: If you tune the top (or batter) head higher, you’ll get a clear, open sound with ringing overtones. If you tune the bottom (or resonance) head higher, you’ll get a warmer, lower resonating sound with more center tone. If you tune both heads to the same pitch, you’ll end up somewhere in between - that is, with a clear sound and tone, and very long resonance. Muffling can be applied to further control the overtones of either head.
Very large intervals between top and bottom heads tend to dampen the resonance of the drum. Tuning the bottom head on a tom somewhat higher than the top head can also produce an effect where the tone 'dives'.
Tune the drums to a pitch where they are comfortable for you to play and fit your idea of the sound. If the snare drum rattles excessively when one or more of the other drums are played, try to change the pitch of either drum to avoid the sympathetic resonance. Sometimes, just changing the pitch of the snare head will be enough.
Snares
The wire mat under the snare drum is called "the snare". It's available in a variety of sizes and materials. In general, you can say that the more wires in the snare, the more it contributes to the total sound of the drum. But it also has the side effect of dampening the open sound of the drum, comparative to putting a hand on the bottom drum head. A wide set of snare wires tend to produce a sharp and crisp snare drum sound, with less of the drum's natural resonance. A narrow set of wires, however, will allow the drum to resonate more, while producing less crispness. You can experiment with different types of wire materials, they decide how the snares contribute to the total sound of the drum with respect to timbre and sensitivity. A good set of snare wires can make a world of difference - you might get the feeling, you've got an entirely new snare drum. But be careful with the money!