I know that F2P members will be restricted to some, if not most of the area's in the forums here in STO. They still need to be a part of the community in some form, and quite a few F2Per's will more likely be new players. They need to know how to do stuff and in many area's, the best way to get information is through the forums.
My suggestion is to create a F2P forums, that can give information to those players to help them along and progress. It'll help them find information on certain missions, or basic controls ect ect. So, can they have something like that set up here in the STO forums?
Firstly, they will be able to read everything. Secondly, they will be able to post if they have spent any money in the C-store. Lastly, I have created a forum for free players and anyone else who wants to use it(see 2nd link in sig).