I'm working on my MR2's paint currently. I did a lot of research on detailing, then I decided to try the cheapest thing first. I just got some terry cloth towels and some 3M rubbing compound. It takes a lot of rubbing, but the results are way better then I expected. I just put a quarter sized blob on a towel, spread it around a 1'x1' area and then rub back in forth in a straight line (not circles) until there is just a haze of compound left. Then I take a clean cloth and buff the haze off. I am going to have to go back over this with a polish or cleaner to get a better finish before waxing. I would say the oxidation on my car is HEAVY, so rubbing compound may be overkill for you. Try a cleaner wax, swirl remover or simply polish. Try the least abrasive stuff first and only go more abrasive if you don't like the results.
I like this last pic, you can see the oxidized section completely diffuses the light, only reflecting half of the garage door opener light where I've used the compound. You can also see the oxidized paint on my towel with a bit of product placement.