I'm currently running CNet 5.07 on my BBS, and have run from 3.05 up to...
I ran 3.05 on an Amiga 500 with no problems at all. Naturally you'll want as much RAM as you can cram into the thing. Also, if you want your BBS to be reasonably smooth running, I suggest running a stock Amiga OS. Nothing that will take more memory then needed.
Also, the bigger the HD the better. If you can max your HD size out go ahead, if you're serious about running a BBS.
Right now there are at least 4 of us, all running CNet. If you're interested, feel free to PM me and I'll give you as much info and help as I can.
BTW: Anyone wanting to run CNet, I believe you can still get licenses from the current owner.