I'd go for the full championship first in most cases, just to see where you stand, unless you feel you need the practice or to work on your setups. This especially applies to the FGT championship
This. 👍 And you don't have to necessarily get all golds, either. Just have the most cumulative points by the end of the event and you'll get the prize money along with the car.
It makes no difference, but as was pointed out you do have to actually do the actual championship if you want credit for completing it and the rewards that come with it. Personally, I do the individual races first for various reasons, like practice or deciding whether or not I'm satisfied with my car's performance for the event.