You've got a lot of options. Fostex, Tascam, Roland, and others make some great standalone digital multitrack recorders. You can also go the Digital Audio Workstation (DAW) route, which means buying audio software and using your computer as the brains of the outfit. I use Cubase and Logic Pro on my Mac DAW, but there are LOTS of choices out there. Be prepared for a steep learning curve if you go this route; the software is very powerful but can also be very complex unless you're already experienced with digital recording.
Either of those two routes will provide plugins that can replicate the sound of nearly any guitar amp at the click of a button. Amp modeling has come a LONG way in the past few years; it's gotten to the point where I can't tell the difference between a real amp and a plugin in a blind test. I record everything direct now using plugin amp modeling. If you go with a standalone digital recorder and it doesn't have built-in amp modeling, you can always use a Guitar POD (standalone amp modeling device) between the recorder and your guitar.
If you're just going to be screwing around you'll probably do best with a small multitrack recorder. Easier to learn to use for a novice and they can do great things in the hands of someone who knows what they're doing. A lot of bands out there have recorded entire albums on cassette 4-tracks.
Here's a link to get you started:
http://pro-audio.musiciansfriend.com/recording/multitrack-recordersIf you'd like to listen to some of the stuff I've written and recorded over the years, click this link:
www.kettletriggermusic.com/Audio
