I don't know if there is an official list of supported controllers. Xbox (360/one) and Playstation (3/4) controllers should work fine, the Steam controller, and lots of generic controllers should work using something like x360ce in Windows or the 360 Controller Driver in OSX.
I used a Steelseries 3GC with an old version of Motion In Joy (there are reportedly better alternatives to the current version). The Wii U controller adapter at least works in Windows with Xinput, but in Dinput mode (required to support multiple controllers) it can cause a crash on startup if the drivers are installed for rumble support. Gamecube controllers have also caused this crash (a general problem in various games with ezfrd64.dll, used for USB controllers or PS2 to USB adapters; a generic USB hub also caused a crash for one person, and Windows 10 in particular seems to have more problems with USB devices that are not fully recognized).
