Dave,
Everyone here has given you great advice! Here in New England, Hubby and I participate in "Corvettes only" judged "show & shines" where cleanliness and condition are judged, generally by 2 judges at the same time, and you are in groups of similar cars (i.e. Roadster or Coupe, same group of years). Generally, there are 3 classes (or more if the show includes "Modified" or "Personalized" classes). First is "Street" where judges touch nothing, they only look at the car from 3' away, hoods/doors remain closed. Second is "Super Street" in which judges go
everywhere but not under hood. Third is "Show" where anything goes, including engine compartment.
Remember, here in New England, these shows are judged on cleanliness and condition...so if you think it's clean, then clean it again!

Alan and I typically clean the cars at home the day before the show, drive to the show, get there as early as possible and then clean it all over again for about 3 hours!!! And people wonder why we consider this fun!:L
As far as tires go, we brush everything out of the treads, wipe them down, and we like a non-greasy look so use "More Shine, Less Time" by Stoner Products. We also like the sheen of 303 Aerospace Protectant on all of the interior. The "greasy, slick" look isn't necessarily a plus!
We both prefer the judged shows rather than participants choice. We want our cars to win a trophy based on its own merits rather than because we have a lot of friends who are also entries in the show and who may vote for us!!
Good luck...have fun!!!
Elaine