Well thats a pretty big question. One thing I would do is a search in the recording section to help with the details. I'll bite though....
Overall pathway for recording....
Drums-------> mics---------> preamps---------> Analog/digital interface------->computer-----> digital/analog converter--------> monitors.
Mics---- Sounds like you have your mics and sounds like you will mic with two overheads, snare, bass, and three toms (8mics.
preamps--- Can get exquisitely expensive with this area of gear. You will need one pre per mic. Separate pre's are wonderful and I have a serious collection habit with pre amps but for most the preamps that are built into the converters (see below) will work just fine.
Mixers--- I let it out of the pathway because it is usually not needed for home recording as you can use the mixer in the software for EQ, compression, gating, bussing, and playback. Don't get me wrong there are a lot of great mixers out there but the one you would really need would be the ones with firewire connection to run each separate channel into the computer. these usually run about 2000 dollars.
Analog/digital to digital/analog converter. Here is the heart of your system and there are ton of them out there. For the price (around 300) presonus is the way to go if you want to save cash. I am thinking the fire studio or M audio's fast track ultra. This is where the rubber meets the road and the analog signal is converted to digital. The word clock reign's supreme here and again you can really drive up the price if inclined (There are converters that are just two channels that can cost 10000).
computer--- check what ever interface and software with your computer for compatibility and horse power
monitors---- obviously important for playback. try to go with monitors to get the closest reproduction of what was recorded.
good luck
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