If you have specific games in mind you can check out this site emuready.com. That let’s you filter by device or cpu to see how well games play, sorta like ProtonDB for Linux emulation.

I think the biggest issue is, are you looking sub $200 before shipping+tax or after. For example I think the Retroid Pocket 5 is supposed to handle gamcube pretty well, but thats $200 just for the device.