It's best to use the lotion sunscreen, those spray on kind are absolutely worthless. Not only do they only protect just the area you manage to spray, and often times parent spray from too far away not protecting at all or too close creating lines of sunscreen, but many people around you usually don't appreciate it. If you say, you only apply it in room, well then you're not providing any protection throughout the rest of the day.
For the fair skinned, apply it heavy, apply it often, and that means you'll be applying it in the park around other people.
Put all your liquids in a gallon ziploc bag for the checked bag, including toothpaste. Although deodorant is usually safe enough to keep in the carry on.
Many times I've brought things with me one way, and had trouble going back the other way. Like the time I had a tube of toothpaste, went through fine coming to Dallas, but it didn't pass going back to Orlando.
I love the spray on sunscreen. We've been using the Neutrogena spf 45 or higher and have never had an issue. Granted, we go through several bottles during a week so it's certainly not cost effective, but I can't stand the feel of heavy sunblock. And don't dare sit in the sand with the stuff on - makes ya feel like a shake n' bake porkchop.
But OP, just throw a couple bottles in your luggage in a plastic baggie.