there are lots of commercially available products for this, but the problem is, there are thousands of kinds of plastics. finding the right one will be hardest, but most will probably tell you on the label what they work best for.
look in weird places like electronics stores or auto stores. There seem to be a lot online, but if you know of a good place and aren't too embarassed, it might be good to take it into a store that sells them and ask for their advice.
this guy restored his ipod nano (incudling screen) with Brasso
http://todd.dailey.info/archives/2005/0 ... of-brasso/
which is not really a plastic polish, but did beautifully on this screen!