Any medium to high end forum is going to need a dedicated server lower to mid you will mainly need at least 4gb dedicated ram and 2-4ghz cpu, if you get like a dual core with 4gb of ram I think you would be fine, but if you get cpanel and run other things that requires ram too, so make sure you set aside 1-1.5gb for things like that.. it really mainly depends on how many people are online at once, and you also need to optimize things like the mysql, forum software, apache, etc..
You should be able to get this for around $100 with cpanel, or $75 without a cp.