I've never used Final Cut. I use after effects and that may or may not be easier to use. I'd suggest that you make sure the green screen is as smooth and wrinkle free as possible(1), make sure the green screen is lit pretty evenly(2), and DO NOT WEAR GREEN OR A SIMILAR SHADE!!!!(3).
For number 1 &2, it is easier for the software to key out the green screen if it is closest to one shade as possible. Having wrinkles and poor lighting can cause shadows to be on the GS which could be a pain when you are trying to key yourself out in the software.