Running the unwashed is very cheap. Any forum is if you can set it up yourself.
We paid roughly $20 to get started, and we now only pay for the domain name, which is also around $20 a year.
Obviously, if you expect hundreds or thousands or concurrent users, you need a faster server, but for most normal uses, a cheap host will do.
Generally, I've found that cheap european hosts are more stable than cheap us servers. Better, and more expensive servers are equally good no matter where you buy it. Again, if your users are 99% american, I'd probably still pick a cheap us server.
Feel free to send me a mail if you have any questions - it's troelsl (at) rsens -dot- dk.
Currently, we are using
http://en.hostzero.dk/ and Simple Machines Forum (SMF)
SMF is IMO the best free forum software out there, although there are a myriad of other forums that are close. Pick forum software that is frequently updated, or you'll quickly find yourself overrun by spambots unless you're willing to modify it yourself.