Many hosts have Fantastico (cPanel control panel) or Installatron (DA contro panel) which installs scripts with minimal user input.

Forums can be hosted on an inexpensive shared account and it probably won't be necessary to upgrade until you have a fairly large number of users.

Free hosting and unlimited hosting versus paid: I would tend to look for a paid host that is not offering unlimited storage and bandwidth. You can find plenty of hosts that charge as little as a few dollars per month that will offer reasonable storage (500 Mb) and bandwidth (5 Gb). Don't sign up for a year, go month to month until you get a feel for the company. Go with a company that offers some sort of time limited, say 20 day, money back guarantee.

Buy a domain outright, don't fall victim to the free domain with hosting marketing tactic. Ensure that your information is used as the contact information for the domains registration.

Free hosting or free forum hosting is not necessarily bad, however, there are features, ie. control panels, script languages, file access, etc., that may or may not be offered with such a hosting account. 'You get what you pay for' applies.