Any time we're staying in a Disney Vacation Club villa with a full kitchen, we make a point of ordering our provisions from Garden Grocer. There's a broad selection of items that might cost a little bit more, but the convenience factor is worth a price surcharge. We usually cook our breakfasts early in the day, so we can get an early start, pack a few snacks and order enough water for our visit. The service is great and we recommend it whenever we can.
We used to rent a car an go shopping the next morning. This was easy, prompt and let us have a full play day.