I’ve had good luck with RetroDeck both docked and on the deck with multiple controllers. Not saying it is always smooth. But at least got it working in some emulators pretty steadily. They have put more effort into controls than I have seen from any other emulator aggregator.
Finding a good client is hard. Folks recommend the Nvidia Shield Pro. Finding something that plays all the formats and can pass audio through hdmi to a AV receiver. Umcompressed HD audio, HDR/10/DolbyVision. Etc.
If I can just pop a debian machine down, that is great, but a hardware guide would be nice to see.