Ps3 controllers are a perfect match for the small layout of the raspberry pi, and can be found quite cheaply.
they have lots of problems reconnecting.
When I turn off my controller I can’t get it to reconnect without a reboot.
Also a sleep function would be nice as to save battery life. I had a windows program 5 years ago, can’t remember name or where I got it that would disconnect controller when idle and also had a optional button combo to disconnect
Xbox controllers work nice but the receiver is way to bulky almost the same size a the rpi