You can bring a med. size plastic tote cooler from home with a few starter items then purchase additional items from any resort store. Fill it up daily with ice from the resort and things will keep ALL week long. Put things in tupperware containers or ziplock bags to keep things fresh and dry. You could bring meats and cheese, cream cheese, condiments, etc. You can get milk daily from the resort in various sizes.
We now own DVC but we used to fix lots of things in our room pre-DVC. We brought pringles (travels real well) cookies , crackers, dried fruit, and fresh fruit for snacks. And canned meat (tuna, shrimp, chicken, crab meat) for sandwiches. We would save the mayo and mustard packets from take out places to mix with. As long as you use the whole can there is no waste or put it in a little container on ice. I also would bring a roll of paper towels and little plastic bowls and paper plates. Don't forget the can opener. They do sell bread in the store. Also a little bottle filled with dish detergent to wash things up in the sink. My old camping days have come in handy for a little creative thinking.
Hope this helps.