Some of the very low cost shared hosting deals are actually a very good bargain. In general these providers will expect your site to use a small percentage of the server resources because to make money they need to host many sites.
I suggest you read the reviews here and look for credible reports from existing customers. A new forum does not need to put much load on a server or have much free hard drive space, so starting out with a low cost shared hosting account is a practical idea, I think very many popular forums may have started out that way.
Some types of forum software place less load on the server, you might want to look into that.
██ Skeptic Hosting
██ Promoting a reality-based lifestyle choice
██ Hosting by invitation only, nothing for sale
Decided to look at TSOhosting, heard very good things about them.
never heard of them actually, just follow these basic guidelines.
1. get an offsite backup service for your account, and ask about backup options they might offer.
2. make sure you order the right plan to support your site code
Linux hosting for PHP + mysql based sites
Windows hosting for ASP based sites.
while windows can run PHP , it's strongly recommended to use Linux for this purpose.