As Peanutuk said, any 2.5" laptop type drive should work. It slots into the A1200 nicely (same as the A600). However, the standard Amiga filesystem (FFS) can only use 4gb of space. I believe if you bought a bigger HD, for example 20gb, 16gb would be wasted, although I'm not entirely sure about this.
If you do want a bigger HD, your best bet would be to get rid of FFS and go for a different filesystem. I believe SFS and PFS support larger HD's, although I don't know which is better (anyone else know? Give a suggestion). I do recommend however, to scrap FFS as early as possible as it only gives you problems in the long run.
Alternatively, if you want to use a 3.5" IDE HD, it is possible but it's not as easy as just plugging up the drive and screwing up the case. You need to delve in a bit more.
To summarise, get yourself a 2.5" HD and, regardless of size, switch to a different filesystem.