1. Public: these would be democratically run forums. The users would actually be able to vote for moderators, and perhaps even rules around them. This would be ideal for things like r/[country] or r/[city].
2. Private: these would be traditional forums run by the people who found them. It should also be possible for the "person" who runs it to be a corporation or similar group.
3. Personal: This would be a users own "twitter" like feed.
Other things I think would be needed are:
1. The owning company be a foundation like wikipedia, run as a non-profit.
2. The data and code should be open, so that if anything happens a clone could be setup.
3. Site wide minimal content rules set by the owning foundation. There are some things that should not be allowed at all.
4. Built in trainable AI agents. Moderation is a huge task and I believe it's on the site to supply appropriate tools. By trainable agents, I mean efficiently integrated machine learning models that moderations can personally update and train per sub to help them enforce the rules.