You're better off NOT to paint plexi. You'll always end up with splotchy, uneven results. Original marquees were screenprinted. The more modern equivalent is to get someone to print out the full-sized artwork and put that behind a plexiglas sheet.
Many people use mamemarquees.com and emdkay.com to do this, or just find a local printer that can do oversize color prints such as Kinko's. If you go the Kinko's route, the Polypropylene is the cheapest and probably acceptable for what you need it for, but the backlit material looks better when lit.