To prevent swirls, apply the polishing compound by rubbing it in with your finger, working it until it turns into a dark gray film. Then hit it with a cloth wheel and a dremel. Then re-apply another layer of the compound and hit it with a microfiber towel. The dremel will get out the swirls and leave a few small streaks, but the towel should clear those up.
I don't know how high of a sandpaper grit you plan on going, but I used a DA and wetsanded up to 1000, then hit it by hand again with 1000 wet, then 1500, and stopped at 2000, then the compound and dremel.
I think they came out alright. They look a little dull in that pic, but that was after a day of driving and I still have to spray the metal sealant on it.