Get a custom board script. That way you can ingrate it so their member username works with the forum (possible option would be choose display names) if you really want something basic and secure (posting, thread starting, quoting, replies) and not much else then its a cost effect route to take plus you know exactly whats in it and whats not. Forums are a simple thing its all the bells and whistles that make them complex.
Everything on the market is so over the top with crap that there isn't a solid suggestion. The basic ones are so outdated and perl based.
www.hotscripts.com still indexes a few of the cgi/perl basic ones and a few(very few) basic php ones.