Disney World is like my favorite place ever! I'm so jealous of you that you get to go and I am stuck here. Where are you staying?
My suggestion is to go online (or get the most recent guidebook from the library) and look at the attractions ahead of time, and pick out the things that you would really like to do in each park. Then do those things first, with the brand-new and very popular attractions first thing in the morning. Then you can fill in other things at slow times or at the end of the day when you're done with your list.
As far as shoes... I am not a tennis shoes kind of girl, I hate them and I only wear them to work out. I did wear flip flops to Disney World, and it wasn't really a problem. As long as you are 100% sure that you won't be getting blisters or that your feet won't hurt, go ahead and skip the tennis shoes. On that same topic, I am not a shorts type of girl either. It will probably be warm, but not so incredibly hot... you could prob. get by with wearing capris or jeans, but you'll just have to wait and see when you get there. I went a few years ago in May, and I actually wore a comfortable, knee-length skirt to the park on a couple of the days, and it was much better than shorts. But that's just me
I'm pretty sure you can bring backpacks and bags into the park, and you'll definitely want to bring water (since bottles purchased in the park are sure to sell for ungodly amounts of cash). I would suggest going for something as light and small as possible... it can be a pain trying to find something to do with your bag on rides and attractions.
I hope you have a great time!