Thanks!
In theory, all of the controllers listed here should be supported. We've only tested 5 or 6 from that list, but so far everything that was supposed to be compatible has been. We haven't tested a PS4 controller yet, but it is listed as compatible.
In the first couple levels there will be some instruction on controls, and it might say A and B instead of X and O, but it should be easy enough to figure out.
The keyboard/mouse controls do require a mouse. A touchpad on a laptop would work to, although it wouldn't be very comfortable.