The Mac Mini would indeed be a nice solution to at-home recording. It's packaged with iLife '05, including Garageband, one of the simpler home-recording software solutions I've used.
Couple things to keep in mind, though: The Mac Mini doesn't have a built-in audio-in jack. So, you will need to get some sort of USB or Firewire based audio input support. Personally, I'm in love with the
Griffin iMic.
Also, as I'm sure you're aware, the Mac Mini doesn't come with a keyboard or a mouse or monitor.
Another option you might consider is the
eMac. Very similar specs to the Mac Mini, except that is has an audio input included (eliminating the need for the iMic), a built-in monitor, and comes with a keyboard & mouse. For a total of $300 more than the Mini.
As an example of what this type of recording can produce with just a guitar & cheap condenser mic, consider listening to my cover of The Police classic,
Man In A Suitcase.