The way I'd probably do it is to buy some royalty free drum loops and load them up into whatever recording software you use. (Cubase, Pro-Tools etc.)
Use a simple 1/4" to USB connector like this...
http://www.sweetwater.com/store/detail/LightSnake10/
... and an amp simulator like AmpliTube.
If you didn't want to go to the expense of buying Amplitube or want to use an amp, you'll need a Mic, some kind of mixer or line level adjustment device (volume control) and basically the same connections or something like M-Audio stuff or whatever you want to convert the MIC or 1/4" plug into USB.
Personally I prefer loops to drum machines because they're played by real players. I also prefer using something like Amplitube because you can record a straight signal in and simulate any amp you want after you've recorded.
If you use a condensor mic, you'll also need 'phantom' power. You can look up what that means using Google.