The best/easiest way to get started with a self-hosted LLM is to check out this repo:
https://github.com/oobabooga/text-generation-webui
Its goal is to be the Automatic1111 of text generators, and it does a fair job at it.
A good model that's said to rival gpt-3.5 is the new Falcon model. The full sized version is too big to run on a single GPU, but the 7b version "only" needs about 16GB.
https://huggingface.co/tiiuae/falcon-7b
There's also the Wizard-uncensored model that is popular.
https://huggingface.co/ehartford/Wizard-Vicuna-13B-Uncensored
There are a ton of models out there with new ones popping up every day. You just need to search around. The oobabooga repo has a few models linked in the readme also.
Edit: there's also h20gpt, which seems really promising. I'm going to try it out in the next couple days.