RAIN PONCHOS! Oh, and water proof footwear!
Crocs are great. Standard cheap flip flops not so great in pouring rain.
Otherwise, it's standard summer fare.
My general tips: avoid denim - esp when it may rain or you are going on Kali or Splash!
Pockets with zippers are best! (Other options like velcro are also okay, the more large pockets the merrier) DO bring lots of cargo shorts, esp the kind that are lightweight fabric.
Avoid shirts (plain white cotton ) and shorts that become see through when wet.

Unless you know it won't rain that day and you won't be goin on Kali or Splash Mtn.
Sunblock.
Farbics like nylon (think mens swimsuits), silk and silk-like polyester are good. Another option that can be good is something like 'dry' cotton (the brand I know about is Nike) or wicking fabrics.
Tank shirts are nice, so long as you aren't planning a Signature dinner. Sometimes a very lightweight shirt with half sleeves is good for sun protection, too!
I found I mostly stayed with sandals, but at least two pairs of good walking shoes per person. I can't walk forver in Crocs personally, but they are useful in rain, at the pool, on water rides. If your senakers DO get drenched, supposedly stuffing them full of newspaper helps dry them. Otherwise, it can take days in FL humidity! (And most likely they will get foul! smelling in the process!)
If there will be afternoon thunderstorms, consider the afternoon break.