Most Bluetooth controllers should work well, and PlayStation controllers should work well over wired.
I couldn't get it to work with mine. The controller works fine on the OS level, but the game did not respond to it at all. Is there any other trick needed there to get it to listen?
(Finished the game on the keyboard by now, and it was great! Keyboard controls felt a bit awkward though compared to playing Wilmot's Warehouse on a controller.)