Gitea is probably the best self-hosted and private alternative to GitHub and Gitlab there is.
Only one problem. Provisioning a box is an hours long PITA. At first you think "this will be quick", but then suddenly you're knee deep in Nginx configs and you can't get the Let's Encrypt cert to take properly and your database doesn't have the right privileges and you're just about ready to flip. All you wanted was a simple self-hosted git server.
That's where we come in. We deploy a fully provisioned Gitea instance in literally minutes.
Your instance gets a nice cozy Linux VPS all to itself, and you get full root access to the box. We manage the OS updates, backups, monitoring, security, and Gitea upgrades.
Want to know more about Gitea? Check out their excellent documentation. There is also an instance you can try out to see how you like it.