Cheap and good mini-PCs for gaming?

Hello, everybody! I want to have a little mini-PC for gaming that operates like a console. I don't want to have a big, clunky case in the back or front of the TV. Furthermore, I don't play many AAA titles from recent years, so the hardware doesn't need to be high-end. It would be nice if I could run Scarlet Nexus, Nier: Automata, and Horizon Zero Dawn at a stable 60 FPS. The graphics don't need to be extreme; I just want to enjoy the game.

Also recommend some great distro's for gaming.