Usually you can find a grocery list on the DVC Member website. At WDW you can get the gift shop at the resort to fill the order. I am sure there are several delivery services for the DL area as well. Bell services should be able to keep your cold things in refridgerators until your room is ready. I think you can just fax the order...I have been in the store when a CM was gathering things for an order.
We go shop and Garden Grocer are the two main delivery services at WDW.