I will strongly go against the other advice in this thread.
Buy your son a PC laptop and one of Digidesign's Pro Tools LE setups (several models with different prices/feature). Pro Tools is a combination of hardware and software, so it covers all the bases and everything will work properly right out of the box. Because it is all included, you don't need to worry about which sound card to get, and the quality of the audio hardware ranges from good to excellent. It will also work on a Mac, but you're going to buy a PC because you'll get more speed for the money, and that will leave more money leftover to get proper audio hardware/software like Pro Tools instead of consumer-oriented crap like the other suggestions in this thread. Pro Tools LE does use the computer's CPU to process audio (unlike the better versions), but almost any modern laptop will have more than enough power.
Pro Tools is the industry-standard DAW (digital audio workstation) package for all professional recording studios. Many (or even most) modern albums use Pro Tools for at least part of the recording process. The tracks your son records in the garage with his Pro Tools setup can be taken to any real studio on a hard drive, where he can add to them, mix them, master them, etc. The reverse is also true. His band can record drum tracks in a real studio, then come back home and record other instruments or vocals later at home. And because it is portable, he can pack it up and take it with him to different rehearsals, or even use it to record live shows. For instance, any given song that my band recorded for our last album included layers of audio from two different professional studios, three apartments, a rehearsal studio, a cabin, and several outdoor locations. We then mixed it in yet another home, on yet another Pro Tools setup. Everywhere we went, the tracks loaded right up on the next Pro Tools setup.
There probably isn't anything intrinsically wrong with the audio quality of the suggestions that others have made, but this is an issue of making sure the recordings your son makes aren't worthless in the future because of compatibility issues. Pro Tools is in nearly every recording studio. For posterity and flexibility, it would be extremely foolish to spend money or time using anything other than Pro Tools.