Typically you can set this up with any webhost that you wish, most will have the features and software to install it. Sometimes the host has automated software that will install/configure the message board/bulletin board software. The one that I can think of off the top of my head is 'Fantastico' which some hosts offer to automatically install the software, and then all you have to do is configure it from the board's admin panel. That way you don't have to deal with installing the files/setting permissions etc.
Also, most boards require a database, the most common type is MySQL. Any webhost should be able to provide that as part of standard features for a web hosting plan.
Do you expect this board to be very busy? Just a word of caution that some forums that are extremely busy can cause a heavy load on the server, which some webhosts don't like. A small forum for high school friends shouldn't be too bad however. Just something to think about.
I would agree with the view that Aviatrix mentioned, registering the domain seperately may be a good idea. The only reason I say that is that it reduces difficulty if you decide that you are unhappy with your webhost and want to switch companies. This way your domain is under your control and you can switch to a different host whenever you wish.