Most of the new fourms start with a shared hosting plan. If they get more users and activity, then will consider upgrading to bigger servers..
Shared hosting is too cheap in these days… you can get some entry level package for $2 per month..and if you are ready to pay a bit more, say $3 – $4 per month, you will get somewhat good hosting plan..
Usually a domain costs almost $10 for an year. But many hosting providers give you a free domain as long as you use their paid service.
If you are planning to promote your forum seriously, better stick with a paid hosting plan than going for a free forum hosting services.