The image coordinate system should almost never be changed. Off-the-shelf commercial drones will tag the images in the WGS84 coordinate system. This includes all of DJI, Parrot, Autel, Skydio, etc. The only time you would ever change this is if you are using a custom drone that could be tagging the images in some other coordinate system.
Your desired output coordinate system and GCP coordinate system do not necessarily have to be the same. Usually they are but you can have the positions of your GCPs in any coordinate system. Just make sure it is correctly specified in the GCP manager. The same goes for your outputs. You can have Mapper output any coordinate system. You just need to specify it corrently.