You should be able to use pretty much any Bluetooth controller just try to avoid the Bluetooth low Energie LE controller my stadia controller that i resenty bought doesn't work on many distos Nobara no problem if you use arch forget it

Both the PS5 and Xbox Series X controllers are very good. I've had some incompatibilities on my computers with older bluetooth hardware though. Speaking practically, I'd recommend the Xbox one as it's slightly cheaper, takes regular replaceable batteries. Subjectively, I prefer the PS5 controller (I like the feel, and the trackpad is really handy), but I've already had to replace the lithium ion battery in mine. (Had to do the same with my older PS4 controller too)