If you also want to host or build interesting social apps, you should definitely do an isolated atproto / Bluesky service! https://blueskydirectory.com/

As for actually doing this... running a PDS and relay isn't that hard, and the red dwarf web client is online and can be configured to point to whatever appview you want. There's significantly less experience running your own appview, but there are options & folks are happy to help.

I’ve used bluesky, and it’s very twitter-like. That doesn’t seem like the best model for a close-knit community. For larger ones, perhaps!

There are projects that make running independent atproto networks "easy": https://github.com/verdverm/testnet

I no longer recommend ATProto, in part because the public by default was a terrible choice. People prefer privacy, not anyone in the world able to read all of their activity. Bolting permissioned buckets on after the fact is not the way, it needs to be core to the protocol design.