Well, to start with, you would need to specify / mention what forum software you are planning on using.
Normally, the forum application will have it's own "minimum" server / hosting requirements. You can than figure out how much bandwidth and disk space you would need as a minimum based on the content of the forum - graphics / text / etc. A number of times, the application publisher will give you guide specifications on this too ..
Start off on shared hosting. If you out grow it, you only need to install the forum software on a new machine then backup/restore your old database and copy across your custom skin. They aren't difficult to move.