Domains typically cost around $25 to register but you can find places that are cheaper. Hosting cost really depends on what traffic you'll be getting andhow much data transfer you want to buy along with the other good stuff like e-mail addys, subdomains, databases, ect. Right now 2GN and TRSN is on a step up from the value plan b/c there isn't a whole lot of traffic to either and enough to need a huge data transfer. If you're going to use it to host large pics, vids, ect... along with a forum then you'd want something with a large data transfer since the pics and vids will consume most of it. A forum and some pics won't do much since the emoicons and all the little buttons plus the php pages aren't that large in size.
When looking for a place to have it hosted look for reviews on the hosting company and make sure they have good support. I used to have this site on
www.doteasy.com and they were teh suck. Every night my sql connection for the forum would go down and they'd keep denying it even when I had logs going back for over a month of it going down every weeknight at the same time and everyone on the forum saw it going down. Just get good reviews on each place you find, you can usually find sites that score each company yearly or so.
A phpBB forum is very easy to setup, VERY VERY EASY (atleast for me it was). phpBB 3 is coming out soon (maybe) so I personally would hold off on starting anything until then b/c who knows if an upgrade to the new version is going to be easy. But you can always install the current phpBB version then see what comes about.