I am trying to get into self hosting. Can anyone recommend a Twitter or Facebook self hosted app? The idea would be that it would be an invite only social network where I choose who can join.
Share and collaborate on documents, send and receive email, manage your calendar and have video chats without data leaks.
For a Twitter equivalent, Mastodon.
Facebook's a bit more of a challenge --- longer-form content, the ability to group contacts, and the like.
Principally there are Diaspora*, Friendica, and Hubzilla, all based on or near the ActivityPub standard.
There are limits and compromises to these, though all should handle small-scale (family/community) sharing easily. Mastodon's at millions of users, the others are probably smaller.
At scale, moderation and administration of Diaspora* is a bit of a pain, though that's (slowly) improving.
So you can set it up as an "invite only social network where I choose who can join", as you say.
Discord is invite-only but not self-hosted. Maybe that would work for you?
scuttlebutt https://scuttlebutt.nz/
twtxt https://indieweb.org/twtxt
iris.to (hypercore protocol)
meshtastic https://meshtastic.org/