@sfriedrich the ps4 controller is supported. You can either use a micro usb cable or sync it up via Bluetooth. To do that, you have to put the controller into sync mode by holding the share and PS buttons down until the light on top starts flashing. Go to the retropie menu and then Bluetooth, and sync it up. It will come up as “wireless controller”, then just configure it as you would any controller in emulation station.
And no you don’t have to use a systems original controller. you can use any controller usb or Bluetooth , including ps3. Retropie makes a mapping for each emulator to use your controller that you are using. You just have to configure it in emulation station.