Hello!
I'de recommend painting the plastic anyway - it will look better this way. No problem if you don't have an airbrush - if you take car spray paint can like DupliColor (I don't know if you have this brand available), you can get very good results if you try painting the body shell with it. It's good to start with their filler/primer first - take filler if you have imperfections to work out or just primer if the surface is nice and even - then go with some thin colour coats on top of that and finish with a gloss coat - preferably all from the same brand. You might want to fill in the seam lines with black prior to the colour coats.
As for chromes - they don't like to be overcoated with nothing, about the same way it is with glass. Clear always takes away some shine, sometimes a little, sometimes a lot. It's good to add chromes at the very end if possible - after all the polishing and stuff. But it's important to make sure they fit well, first.
Good luck with your build and have a nice day
Paweł