The A600 is basically an A500, with kick 2.0x, ECS chipset, 1mb chipmem and IDE controller all stuffed into a chopped-in-half A1200 case...
You'd have to get a laptop (2.5 inch) IDE HDD if you want fit it inside the case - otherwise you might get a converter for a standard 3.5 inch IDE but it won't be pretty.
I think any HDD under 4gigs will do - and if you have/plan to get 3.1 roms (see
www.amigakit.com) and install OS3.9 (also on amigakit) then you can do without the 4gb barrier.
Another interesting possibility are IDE-to-Compact Flash (memory cards) adapters. You could use a memory card as a HDD, which means that your A600 will be quiet (and loading generally fast). However, memory cards have a limited life-span (number of writes), but that shouldn't be a problem with a stock A600 (i.e. you are unlikely to kill a CF card, since the kind of tasks you are likely to be carrying out won't require much writing). You could even mount the CF card externally and use it to transfer files between your A600 and WinUAE see this cool hack:
http://www.amiga.org/gallery/index.php?n=2041=10oh and welcome to amiga.org! :-D
(psss did u check Aros?)