Quick Controls Controllers work in game, but NOT in the menus.
ONLY mouse and keyboard work in menus currently, but you can switch to a controller once out of the menu.
No weapon input, ship auto fires weapon W A S D / Left Controller Stick -> Movement Mouse / Right Controller Stick -> Camera Shift / Left Trigger -> Sprint Space / Controller Up Button (Xbox Y) and RB -> Move Upward CTRL / C / Controller Left Button (Xbox X) and Right Trigger
Enjoy <3