I've found both an a3k and a4k for around $300+sh.
An ethernet card typically runs around another $100 or so, based on my experience. The ariadne is my favorite so far.
The a3k is pretty beneficial if you don't need a graphics card but just want the scan doubled. However, I'm in the same boat as you regarding IDE. I will say that a fastata mk v works well in an a3k and can be had new from elbox, as opposed to trying to find a scandoubler/flicker fixer for the a4k (you'll probably be stuck getting something used). So, that's my $.02...the a3k should be fine for bbsing. I have run amiga express on an a3k with no issues.
Another note...what bbs?

And what software?