These are some building idea mostly for lore really and immersion.Keep in mind some of these have already been posted and I know it will take time to implement these if you decide to add them.
First off I think a church would be nice, maybe it could start off as a small chapel and make its way up to a cathedral.
Barracks or outpost: I think these would be good ideas if your a guard or a soldier for a faction.
Bigger schools for larger cities would be nice like say a university.
A tavern would be good too. I know we can use other buildings for this but a building type for a tavern would be nice.
A jail/prison would be a nice add for the MMO release i guess. This could be balanced by saying people can only be in prison for a limited time.
A palace or castle with a throne room inside it would be cool too if you want to make that type of faction with a king or duke at its lead. You can make thrones already so why can't we have a throne room to put it in?
I'll add more to this post as they come to mind.