Hi Sarah,
What a great vacation you have planned! Your best bet is to grab a car at the Orlando International Airport. You will have more flexibility renting a car at off hours than using a car rental company which is onsite at Disney who has limited hours.
If you do use the car rental onsite at Disney, they will send a shuttle to pick you up at your resort. However, I have found this service not up to Disney standards. Please note that Disney does not own or operate the car rental company on the property.
As for 24 hour shopping, your best bet is a Walmart which is near by. This will have not only groceries but tons of other items you may need for your trip such as toiletries, clothes or suntan lotion.
There are other grocery stores such as Publix and Albertsons however they are closed during the overnight hours.
Wishing you a magical vacation!
Beth