I'm loving this thread, as I made the transition from Mickey t-shirts and cropped pants to skirts and dresses at DLR over the last couple of years. I generally wear cotton blend knee-length dresses or skirts with t-shirts. And I second the comment about pockets. I'm really into Disney bounding, and will do a black and white striped or polka dot dress with red leggings; a combination of a blue/red/yellow t-shirt and skirt, etc. I go on any and every ride, and have done it all (including water rides) in dresses and skirts.
I've done both bike shorts and no bike shorts. It really just depends on how hot it is. I also frequently carry a pair of leggings for cooler mornings and nights. But something as basic as baby or Gold Bond powder can help with any thigh rub if you're not comfortable with bike shorts. And it sounds like lots of other comments have recommended Body Glide as well, which I think also works great. As others mentioned, just try products out ahead of time to make sure they'll work for you.
For footwear, I frequently wear saltwater sandals. I wear them all the time, so they're broken in and comfortable for me. I think that's the key—wear any pair of shoes you like, as long as they're comfortable for you. With that said, I'm a huge fan of a mid-day shoe or sock change to keep the feet happy. Any pair of shoes can be uncomfortable after that much walking. And while sandals are super cute with dresses and skirts, there are tons of cute sneaks that are comfortable, too, and even in Disney patters. Vans and even Target have canvas options, and New Balance does a line of Disney-inspired running shoes for RunDisney.
Have fun!