I highly recommend spending $160 on a dewalt 849x to equip with 2" and 3" backing plates. I use the 849x far more than any other tool because it's smooth and it's so versatile and easy to switch out backing plates and it doesn't require a wrench to do it. If that is a bit too intimidating and the Ibrid nano is out of your price range (it's out of mine) I bought the new BOSS micro rotary and I am EXTREMELY impressed. It doesn't use much air, it's quiet, and it's officially the smoothest polisher I've ever used. Unfortunately Griot's 3" Pneumatic orbital is junk, I bought mine a few months ago and the backing plate broke and before that even on low speeds it would make my hands go numb within the first 30 seconds of polishing and it made horrible sounds and I couldn't put a drop of oil in it without it getting all over my hands when i turn the tool on. BUT the Griot's BOSS micro rotary is a WELL BUILT tool.
If you are convinced you need to stick with DA the cheapest option I can recommend is ordering a Chicago Pneumatic pistol grip orbital polisher/sander. It's $100 and it comes with a 2" and 3" backing plate. I use it for sanding headlights and occasionally for polishing tight spots on thin paint when I don't want to use a rotary. Good luck to you sir!