I agree with a PP about putting sunscreen on at the resort then reapplying again at the park. The first batch at the resort gets to soak in and then reapplying adds another layer of protection. Make sure it is at least an SPF 50 and waterproof. I like the stuff made for Babies because it doesn't sting my eyes. Get everything, especially ears and nose. They have SPF 50 lip balm too. Reapply as directed. Even water-proof only protects so long, especially if you are towelling off occasionally.
The first time we went to the WPs I put the sunscreen on when we got there and didn't reapply. I was so red and puffed up like the Pillsbury Doughboy. The sheets on the bed hurt. With doing it the way I suggested above, I haven't had problems since. I haven't tried any of the shirts, but I may try that too next trip. Nothing makes a trip as miserable as a sunburn.
Also, remember to apply sunscreen when going to the regular parks. The sun can be brutal there too. With all the concrete to bounce its rays off of you can get a burn really quick.