I don't mind answering - I hope the others don't mind - it's just that I know so little that I like the opportunity to show off what I do know sometimes. I'll probably get this wrong, though.
There are two main advantages of recording at 24-bit rather than 16-bit: first, 24-bit can handle a much greater dynamic range, and so you don't need your recording levels so close to clipping all the time, and you can catch more of the quiet parts without hearing noise on the track. Good. Second, if you listen carefully, you can hear the difference between 24-bit and 16-bit: 16-bit sounds kind of grainy, or raw, by comparison.
As for sample rate: as Bruce pointed out, CDs have a sample rate of 44.1, not 48. But you can record (if your system can handle it) at almost any sample rate you like: 44.1, 48, 88.2, 96 - but when it comes time to burn your stuff to CD, you have to make sure everything's been converted to 44.1 if you didn't record at that rate. What difference is there in the sound between these different rates? I don't know. The only ones I've heard myself are 44.1 and 48, and I can't hear any difference, nor can many others who report what their ears tell them. However, despite the fact that I haven't heard stuff recorded at 88.2 or 96, I'd be willing to bet you can hear the difference, and that it's worth doing if your system can handle it. Again, if you record at the higher rate, you have to convert it to 44.1 before you burn it to CD.
All of which is one reason why loads of us would like to see the world start buying more DVD players, because DVD players can play stuff at the higher resolutions, which means better sound.