I agree with @
NLS8520, a PC7424XP (or meguiar's G110) with a meguiar's 5" backing plate, meguiar's 5" cutting discs, and meguiar's microfiber correction compound is what you want to use for buffing the car.
Buffing by hand will only produce bad results. You don't want to use any lesser of a buffer than the recommended PC, it is basically what's in a detailer's starter kit.