Hi Markisha,
When we are touring Walt Disney World, we generally carry a backpack for the day. In the backpack, we have water, snacks, rain ponchos and other items we may need for the day. We try to use a backpack with only one or two compartments as all bags are subject to being searched. The less pockets, the faster the search.
You can bring a cooler into the park. However, rolling coolers and backpacks are not permitted in the parks. A soft sided cooler is generally what you see in the parks. Wagons are not permitted either.
You want to remember that you do not want something so big it will not fit in the ride with you.
Lockers are only at the front of the park which is not always convenient to return to during the day. If you do not have a stroller to use to hold your gear while on rides, you will want to go smaller.
Wishing you a magical vacation!
Beth