A good compound available over the counter is Meguiars Ultimate Compound..
Meguiars also makes an Ultimate Polish to follow up after using the compound..
Just be careful as the amount of paint on the existing plastic parts is always way less than on the metal parts..
Also, plastic does not dissipate heat very well at all and if it gets too hot, it can delaminate off in big amounts..
If I was going to do this and was new at it I would want to keep the compound and pad moist enough so it did not dry out but instead worked longer, so it could finish better.. Wipe it off a lot and look at the work as you go.. Dont try to do it all in 1 pass...
If you are more experienced with products and machines, we can suggest other products as well..
Good Luck !
Dan F