It's easy to run your own instance. Mastodon provides a docker image, provided you have a server or VPS that can handle its asset compilation. I think you can get by with 2gb minimum. You can filter any instances that you don't want to federate with.

I'm not sure what you mean about not being listed on lists of instances. If you mean not federating your own instance, well, that goes against the entire premise of the fediverse / federation. Running your instance means it will propagate. Your posts will show up in the instances of whoever is following you.