My Challenger was repainted in the early 80s also. It had light to moderate oxidation and small surface scratches, I used Meguiare's ultra cut compound (105) and a DA polisher followed up with their cleaner wax. It's not a base/clear shine but pretty good for a 30yr old cheap single stage paint job.
If you can find a Meguiare's or Mother's rep in your area, sometimes they will be willing to use you vehicle for a demo and the you get it done for free. A friend of mine got it done a couple of years ago.