I'm a Rupes fan and have more polishes and pads than I care to admit.
You've got several different choices as most manufactures each have a polishing machine offering. I'd advise yout to stick with a Dual Action polisher as it's the least likely to burn through your clear coat like a Rotary polisher. One of the easiset polishers and the one many detailers and enthusiasts go with is the old school
Porter Cable 7424XP. I still have my 15 year old PC 7424 and it still works great.
For a big box store option and since price is a factor, consider the new Harbor Freight 6" DA made by Bauer. I picked one up for the daughters boyfriend (so he stops asking to use my machines) and got to play around with it. It seems like a decent machine with good value, ergonomics and power. It did exhibit a bit more vibrate than I'm used to but that's to be expected from a lower priced machine. I would probably switch to a 5" backing plate for a bit more correcting power and manuverability as persoanlly I find 6" pads to be a bit akward. Check it out...
Amazing deals on this 20Mm Random Orbit 6In Da Polisher/Sander at Harbor Freight. Quality tools & low prices.
www.harborfreight.com
The real magic comes with pad choice and compound. Several options including some from Adam's that won't break the bank. I think you can pick up Meguiars M101 at any of the major autoparts stores to keep it easy. Works great but can be a little dusty.
Good luck!