First up, I also hate the way there isn't much good resources online. What I know is gathered from many different threads on various forums (and I don't even know how valid the information is). I'll just post what I can remember offhand here. Others can correct me if I'm inaccurate.
Like many others have said before, use the heads. Heads (the skins) have a huge impact on the sound. Whether it's thinner or thicker, coated or clear, etc... if you have the budget, go get a few and try out. But the normal one for snare is coated batter head (the top head), sometimes people also use the one with a "dot" in the center (you can see like an "extra" circle of material stuck on it)
Then learn to tune it. I've never used the drum tuning bible xD I learned tuning in orchestra, and just practiced at it until I know how to get what I want. It's usually quite intuitive lah, if you want it to be higher and tighter, you screw it tighter. If you want it loose and deep, you loosen the skin. After a while you can get the feeling where the head is not evenly tensioned all round, then you can get the feeling for which part of it is too tight or too loose.
Don't overtighten. If you can't get the sound you want from the snare, try adjusting the other head as well (sometimes the top head might be in a good tightness, but the bottom isn't, or something like that). If you still can't get the sound, maybe you're using the wrong kind of head. Usually, thicker and heavier heads (like Remo Emperor) are deeper and drier, thinner heads (like Remo Ambassador) can "sing" more.
Another big problem about tuning is that if your drum is near other drums, and depending on what room you tune it in, you can often hear a lot of off-tune notes and stuff from the resonance. If your tuning problem is that the sound is just not satisfying, then I think you probably change heads (or worse case, change snare) is the solution. But if your tuning problem is that it keeps seeming like a bit out of tune (but the sound timbre itself is nice), then what you should do is move it to another room or something first and play around with it.
Snare wires... usually as long as they're in good condition it should be fine. Sometimes you might get buzzing, or you might feel it's not sensitive enough, etc. This might be because of the drum shell itself. I've never tried changing the snare wires, so I'm not too familiar with this.
Then there's the shape of the drum also. If you want the "crack" sound, I heard thinner snares are better (like 14" by 3"). Deeper snares (like 14" by 8")can get the "pop" kind of sound more easily, apparently because it takes longer for the hit to "reach" the snare wires below, so you hear the drum a bit before you hear the snap of the wire. Wider drums are lower in pitch than narrower drums (usually, but this depends on tuning and stuff)
The thickness of the shell also affects. The heavier and thicker the shell is, usually, the more powerful the sound is, but it also usually means that more of the sound comes from the head, so it's not so complex (apparently). I personally like my thick snare shell (1.3cm thick), but many people don't really like thicker shells.
The shell material will affect the sound. There's many many different materials and types. It's crazy to really memorize all of them, but I think a general guideline is that wood is more "dry" and metal is more "wet" and ringy. There's a lot of exceptions though.
http://www.drumsolo.cc/snare_drums/snare_gallery/snare_gallery.html <- this website is sometimes referred to. Personally I don't *really* trust this, since even with the same material you can get very different sounds with different heads, thickness, size, etc... but I suppose it can give you a rough guideline. If I'm not wrong, the tests from this page was done with segmented shells, which I haven't seen in Singapore before. All the commercial shells I see are ply shells (means they stick together a lot of thin sheets of wood to make a shell), but these are like solid blocks of wood stuck together.
Common "good" woods are maple, birch... most of the exotic woods on this page you can don't expect to see in Singapore-sold drums. If you really want these you'll have to go order them from overseas but I think there's no point in doing so. I personally find that while the material is important, it doesn't make THAT much of a difference to warrant special prices.
Heads and tuning you can use that on any drums. It really makes a huge difference. I changed out the stock heads on my entry-level drumset and it sounded so much better. But if you want to change your snare, you should really go down to the shop, tell them that you're looking for a snare and ask them to let you try the snares and stuff. Haha I don't know if sweelee allows that, though, I bought my snare during the halfprice sale so it was very rushed. Sometimes when I pass by, I just tap the snare drums and it doesn't sound like it's very nicely tuned while they're on display =/ so I don't suppose anyone actually can take them down to tune and test out (I've never seen anyone do so, either)
