"dedicated server" prices can range very very widely depending on configuration and bandwidth allowance.
but as was suggested above, you have no way of knowing your forum will be large until it's actually large. start with shared hosting and upgrade when needed.
don't be one of the fools that spend buckets of $ on the technical aspects of their websites (e.g. hosting) before they have a single visitor. spend the initial $ on marketing efforts if anything.
this sounds trivial to some, but i've seen so many internet newbies spend THOUSANDS on custom programming, top notch hosting and the like, without having a single clue how to attract visitors. it's money down the toilet.