Assuming you're happy with the tone of your amp, there's really no reason to change. You can simply mic it with the workhorse of all mics, a Shure SM57 which can be had for around $80. Shop around, as for that price you might be able to score a free stand and cable.
In terms of recording, you have several options ranging from a cheap 4-track cassette box to an all-in-one dedicated hard disk recording unit to the PC route. Assuming you already have a decent PC (Pentium III or so, 128 MB RAM, > 5-10 GB free disk space), you might want to get your feet wet right on your computer as you've already acquired the biggest expense item (the computer itself).
You'll simply need a audio / MIDI sequencer (many available from the likes of Cakewalk, Steinberg, etc. - plant to spend less than $100) and a decent soundcard. If your soundcard doesn't have a break-out box with XLR inputs, you might want to consider a cheap mixer (I'd personally recommend Behringer - small four input mixer is around $70).
Anyway, I'm sure you'll get a ton of opinions on this and can find a lot more detail on any of these options right here in past threads on the forum - these are just a few quick thoughts to get you started. There are also a ton of great resources on the web - topmost in my mind is
www.prorec.com which has a lot of traffic and a ton of knowledgeable forum participants.
