I second the suggestion of fanny packs. We're coming a few days after you for our first Universal visit, and we got fanny packs for our whole party since (I've heard) some rides ban backpacks but allow securely-fastened fanny packs (they have to have 3-prong buckle). Our strategy is put the emergency poncho, phone, etc., in the fanny packs and skip the lockers for those rides! Note, some of the more intense coasters like Velocicoaster won't allow them—nothing in your pockets, no fanny packs, no nothing.
Meanwhile, I think we'll miss the rain, but personally if I were facing a full day of rain, I'd go for quick-drying clothes (hiking wear is probably good), paired with an extremely lightweight rain jacket that can be stuffed in a backpack/locker when it clears up. I have one made for running that's extremely packable. And personally, I know of no misery worse than wet feet, so I'd pack several changes of socks, preferably a wool blend, in ziplock bags, or maybe just wear sandal-type shoes, perhaps with closed toes.