I have an RX6800XT and I use KoboldCPP to run models I download off of Huggingface.
I'm not sure how many tokens per second it generates, probably about 10?
If you want to try it yourself here's a link to the Github page: https://github.com/LostRuins/koboldcpp
Cheapest would probably be the Raspberry Pi/Orange Pi route.
I gave up trying to make an HTPC (using Kodi, ChimeraOS, etc). It wasn't worth the hassle and ended up settling for an Apple TV.