If you bring your own towels, don't bring special ones. Esp with Disney characters on them. Sadly there have been posts of the towels being stollen off lounge chairs. Sad to think there are some less then magical people at Disney.
I may be getting paranoid, but when I'm at the beach, or pool I always try to face my chair to keep an eye on my stuff. Not that I keep valuables in my beach bag, but sometimes a camera.