Any kind of 'sponsorship' is a business 'partnership'. Your potential 'sponsor' will want to know what and will EXPECT a 'return' on his investment. YOUR job is to present an attractive 'business name exposure' package that does just that.
Best way is to approach your potential sponsor and ask them how you two could work together to get what you each want out of a sponsorship deal. If you make promises to show the car at local car shows or at the sponsors establishment, etc., YOU BETTER KEEP THOSE PROMISES and then some !
If you are wanting a paint job, I'd keep your request at a very BASIC color/design until you can show through a full season of racing/showing, that you will keep up your end of the deal and just MAYBE they will spring for a more showy paint job for NEXT season.
Remember that custom paint jobs can run into the several THOUSANDS of dollars.And that equates into a TON of work and TIME by the paint shop.