Hi Lyndsey! It is great you are already thinking about the walking that you will do while on your Walt Disney World vacation. Many guests just throw a pair of old shoes in the luggage without thought and their feet pay for it after a day or two.
There is not one specific brand or style that works best. Every individual has a favorite style and fit and with all the choices out there now you can certainly remain fashion forward without making your feet suffer. A sports shoe such as a sneaker gives you the most support possible. The down side of a sneaker is on a rainy day. If they get wet they can take a long time to dry so it's always good to have some sort of rain shoe on those days.
I prefer a shoe such as a Skeecher which has the memory foam support. They come in all kinds of styles and colors. Many are slip on but often they have some sort of strap. This comes in handy when you are on a ride where you feet might be dangling and you can risk losing your shoes. Soarin actually asks guests to remove their shoes if they are slip on without straps.
You have mentioned you want to wear a sandal so if you do choose to go that route try to find one that has some support. Flip flops do not support and would not recommend. Clarks and Easy Spirit are two brands that try to not only have fashion in mind but also your feet. And as I mentioned above make sure you bring two pair of the shoe of your choice so if one gets wet you can let them dry out while you wear the other pair.
My last piece of advice is to pack many different sizes of bandaids and also some mole skin strips. No matter how comfortable your shoes are at home you will be walking miles in the parks. I average anywhere from 5-8 miles a day. Your feet will appreciate all the care you can give them. Check out the Disney website for the
Park maps to get a good idea of the kind of walking you will be doing. Have a great vacation!