When we go to Disney, we always order groceries ahead of time and have them waiting for us at our resort. This is a super simple and convenient way to save money and time at Disney World. First of all, we can eat breakfast in our room before we head out (except for the day we do Tusker House breakfast which is a must!).
We also buy snacks and bottled water to take into the parks with us. Disney will allow food and drink to be brought in and it's way cheaper to take in your own water than it is to buy drinks at the parks. I have a slight caffeine addiction so I buy flavor drink packets that include caffeine. My family appreciates that as they don't want to be around me when I get a caffeine headache!! I also bring non-caffeinated ones for the kids since they haven't become addicted yet. :)
I also pack a sharpie to bring with us and each morning, I put the boys' initials on a bottle. That way we're not all sharing germs. Don't forget your backpack to carry the water and snacks!!
If you're in a villa or Fort Wilderness Cabin, you'll have a full-sized fridge so order all the groceries you'd like! In standard resort rooms, you'll have a small dorm-sized fridge so think about what you really need to refrigerate. And I wouldn't do anything that needs to stay frozen as it may or may not have small freezer section in your fridge.
Each night when we returned from the parks, I would put in the water for the next morning. Of course, I had a few Diet Cokes in there and some milk for the boys. So you don't have a ton of room but if you plan ahead a bit, it's great.
Here are the things we ordered for our trip just to give you an idea: