what type of paint is it? spray can? or acrylic? different paint type has different ways of removing.

if it is water based, soak it in window cleaner. if it is spray can, soak in brake fluid. dot 3

test on runner first if you have to be double sure it won't damage your plastic.

otherwise? use modelling thinner and wipe slowly, or sand all old paint off.

its a car, so you want to prepare it to be as smooth as possible before painting. no need to polish, but do sand it properly first. start with a 500 girt, then 1000 grit, and finally maybe finish with a 2000 grit.

prime it once, then if everything looks ok, go on with painting it 

just to add, after soaking it in brake fluid, you will still need to use a toothbrush to scrub it a little bit. use gloves. brake fluid is nasty stuff!