Depending on how established the site is and how many images are hosted on the server, a forum can use from 50-150GB/mth in bandwidth. Having 200GB is a safe bet as you can optimize images to use less bandwidth.

As for RAM, also depends on the size and traffic for the forum. 512MB-1GB is what you should be looking at. If the forum is completely unoptimized, then 1.5GB should be your choice.

As for pricing, a moderately priced VPS is around $40.

A VPS is much different to shared hosting as with a VPS, you are required to handle all the software installs, updates and troubleshooting/optimizing etc.
If you think a control panel will help you, get DirectAdmin.