Hello Spotter,
I have a hobby of making military models-plastic kits and scratchbuilds made of different kinds of plastic,so I have a lot of experiance in painting plastic.
First of all,if you don't know exact type of the plastic which you want to paint,I reccomend that you don't use classic oily based paints.Oily based paints can react very strange with some types of the plastic.For example if you paint ABS plastic or PVC plastic with oily based paints,they react with that type of the plastic surface causing coat of paint which will never dry completly.Coat of paint can even seem completly dry,but after a few months,the reaction with PVC surface will make sticky coat which will never become completly dry.
The best solution will be to use water-based acrillyc paints.They are inert in reaction with every type of plastic.You even can use any of water-based acrillyc paints as a primer in every plastic surface.And after that coat of acrillyc primer has dried,you can paint it even with oily-based paints.But be sure that acrillyc water-based paint has covered your plastic surface completly.You can put two coats of that acrillyc paint to be sure that it has covered plastic surface completly.
Acrillyc paint is dry after a few minutes,but leave it for a couple of days before repainting with oily-based colour of shade which you need.
Other solution,without using any acrillyc primer as a necessity is to use two-component epoxy based paints.They are inert in reaction with any kind of plastic,but they are more expencive than acrillyc paints as a primer and oily-based as a base paint in the shade you need for your restoration.
I hope that will help you,
Regards,Goran