I have been doing a simlar thing for my (rock) band quite a while, with good results.
Our drum kit is simple : bass, snare, 2 x tom, hi-hat and cymbals.
When recording for studio work, I use 7 mics :
Bass, Snare(above - to get the drum note) and snare (below- to get the actual snare), Tom1, Tom2 and a pair of "overheads" above the kit, about 4 or 5 feet away. They catch everything, but are intended for the cymbals.
When recording a live performance, we need to record everything including 3 x vocals at once so I go for a simpler drum setup, with separate mikes for..
Bass, Snare (top only), and 2 x "overheads". Normally the only convenient place for the overheads is against the wall above the drummer, so about 5 feet diagonally up & out from his shoulders. (I did consider gaffer-taping them to his nipples, but he liked it too much)
So that's 4 x mics for the kit.
When mixing both setups, normally the best sound is gained by using the overhead mics as the main source, then embelishing with more bass/snare/toms as needed to make it fuller.
However, to be honest the simpler setup normally sounds every bit as good as the "studio" setup, it's just the studio one enables me to tweak it a bit more.
From this I have learnt that, unless you want to go nuts with 30 tracks just for the drums, it's best to see the kit as an instrument as a whole, and try to record that, rather than as several individual pieces.
One last point .. I have also recorded our band with just a stereo pair of mics for the whole thing. They were set about 10 feet diagonally forward and left/right, at about waist height just in front of the PA. The sound was great, particularly the drums. Nice stereo wideness and lovely tone, especially the bass drum. I think this is behause the kit was on a drum riser (wooden box) which helps with the resonance of the kit, and the room was quite softly furnished meaning no bashy reverb.
Hope this helps