First you need permission for wherever you plan to have the show. Then what we did was solicit sponsors from local businesses to cover all of our costs. We had one large sponsor, which was a local dealer, that had their name prominently on all show stuff like the fliers, shirts, etc. Then we had a few minor sponsors, and then the majority of the rest gave $50 to cover the trophies and such. I think trophies cost around $5 each. We had about 25 categories ranging from antique to newer cars with a stock and modified for each. The majority of your cars may come from the 60'* to 70'* so probably half the trophies were for those. Maybe you could have a trophy for each make, or whatever. I can give you a more detailed list of what we had if you want.
After that it'* pretty easy. You'll need a good number of volunteers to help. You'll want to start about 7-8:00 in the morning to get set up, especially since even with a 10:00 start time, you'll have people arrive at least by 9:00 if not earlier. Have a form for entrants to fill out so you can get their contact info if you plan to do this again. Also info for the car they brought so you can get them in the correct category. We had judging done by all car owners, but I've also seen shows where anyone including spectators can cast their votes. Then we also had a best of show that was judged by a small group (I did that last year, not an easy task). Also if you plan to do an owner/spectator judging make sure to have a cutoff time of like 12-1:00 because you'll need ample time to tally up the votes.
You also probably want to contact the city if you plan to do food. It might not be necessary if it'* at the mall or on campus. But you'll want to ask the mall people since they might not like that. Or they may want a piece of the action.
As far as advertising, it will be pretty hard for you having it so early. When it'* later in the year you can hit other car shows and drop fliers in the cars there. Otherwise just get it out there wherever you can.
As far as they entry fee, I think $20 is a bit steep. Most are $10-15 at the most unless it'* a really good/big show. We charged like $12 at the day of the show, and $10 for early registration.
2003 Black SLE-Stock
2000 Mercury Mountaineer
1968 Oldsmobile Cutlass Convertible-455 cubic inches of muscle