I'd imagine there are programs to bind controller functions to various keys if they don't support it. I'm not sure if there's any program out there to map that mouse to control sticks though.
The wired 360 controller should work with any Games for Windows title. The wireless one can work too, but some systems don't get along with it, it is not the game's issue. Using something like Joy to Key it is possible to map another aftermarket controller to work, but it is a real pain.
And, your right, it is difficult or impossible to map the Mouse to the Joystick on games that don't have it built in, but this game should have that map built in for use with the 360 controller Getting it to work on another controller will not be fun.