Kyle,
You can pick up any Analog mixer. Guitar Center's and such sell 8 or 16 channel mixers starting at $100 - $500 bucks depending on what you want to spend. Yamaha makes good mixers that I've used.
You can plug in your computer via USB with some of these mixers and it shows up just as a sound device you can record with from your software. Something like this, but with 8 channels (should be half the price):
http://pro-audio.musiciansfriend.com/product/Yamaha-MG166CXUSB-16-Channel-USB-Mixer-With-Compression-and-Effects?sku=630258
Also, SHURE makes drum mic packs that are perfect. Check this out: http://www.uniquesquared.com/servlet/the-83/Shure-DMK57-dsh-52-Drum-Pack/Detail
The Beta 52's and SM57's work very well. I also use Beta 98's (small condensor mic's on my toms) and AKG C414's on my overheads. I've used AKG C1000's on my overheads as well and they work very well. Just about any mic's will do, you just gotta know how to tweak the sound from the mixer on.
Here's the latest recording I did with my setup in the drumroom:
https://drummerconnection.com/users/drumfreak/media/audio/5861-gajate-and-cowbell-left-foot-cowbell
Have fun! This is a whole new journey with drumming!