dbowers,
in general, you can look at recording in the following phases to help you understand what basic equipment you will need to start your recording endeavors:
1) Basic Recording: You'll need microphones, at the very least two for recording in stereo. Although you can get by with two mics to record drums, a much better sound will be obtained by four or more, each placed for the most predominant instruments in the kit: the hi hat, kick, snare, and toms (at least two mics for toms if you want to record tom fills in stereo). Don't forget mic stands to position the mics. An overhead rack for the drums, adjustable boom stands and smaller ground stands for other purposes.
You'll need mic preamps to raise the level of the microphone signal so that your other equipment can handle the recording signal properly. Your mixer may already have preamps built into it, but more often than not, a good stand alone preamp will be of higher quality. You'll obviously need to use a preamp for every signal picked up by a microphone, so depending on whether you record one track at a time or several at once you may need to get more than one preamp, or a dual preamp rack, or use your mixer to combine signals to one or two preamps.
You'll need a multi-track recorder to record your music onto. These come in a few different formats, depending on your needs: cassette tape, super vhs (e.g. ADAT), mini disc. You can also use a computer, provided you have multitrack software, a good chunk of RAM and disk space, and a good soundcard. Varieties include 4,8,16-track recorders. For computers, the only limit to the number of tracks is the RAM, disk space, and processing power.
2) Mixing: You'll need your mixer to combine all the tracks you recorded down to a two track format. Here is where you play with fader levels, eq, reverb, delay, and basically getting the mix to sound the way you think your audience will want to hear it. You'll need cables too. Lots of them. But try to keep cable runs as short as possible (even when recording).
You'll also need another recording device to record your mix down to, hence the term mix-down deck. Again formats vary: cassette, vhs, dat, cd. I don't recommend DAT since not many people caught on to the format. The preferred format would obviously be CD, so get a CD burner or use the one on your pc.
3) Mastering: This is where final adjustments are made to your mix to give it polish and refinement. This is better done by a mastering professional, unless you just want to learn how its done, then be prepared to spend major $$$ and many years learning..
4) Packaging and distribution: though you can do this yourself with label software and your CD burner, you can also get it done in greater quantities in faster time by sending your master to a mastering house.
For specific brandnames of the above equipment, crack open a music catalogue and spend time with the search feature at this site.
Cy