Software: phbBB forum is, to my knowledge, the world's oldest and probably most used forum software. I was a MODErator many, many years ago, so I have some experience. It's free, a bit old-fashioned, but that's what I know and don't have to spend time getting to know.
The advantage compared to FB is the clarity. It's pretty easy to find something within certain topics. FB is deliberately chaotic in general. Anyone can write all sorts of crap!
I hope you can easily see the advantages of this forum over FB: Clarity, divided into categories and topics like the structure of a disk on computers. A category contains one or more forums, each forum can have subforums, etc. like the folder structure on a disk.
Fakebook is intentionally made as uncluttered as possible. Most posts on FB are like flies - they're gone the day after tomorrow. FB was made for various reasons. 1) solid monitoring of system critics 2) pastime and entertainment for many who lack a life and 3) gives an impression of the popular resistance to the Elite - did you think that FB was made by kind souls for the sake of your blue eyes? - and even free?