After all of your advice, I looked around. Adam's sh*t's really expensive but all the reviews for it are gleaming. So maybe I could just get:
Adam's Basic Wash & Wax Kit
...and:
Adam's Swirl & Haze Remover Car Polish
...for the swirls, just to keep it all same-brand. But then again this is a LOT cheaper:
Starter Car Care Kit - Cleaners - Car Washing - Car Care - Griot's Garage