We have used wegoshop.com 5 times and are very pleased with their service.
You create your own grocery list, naming brands, size and quantities of what you want. You can stipulate if you will allow substitutions or not. I had Marge Peck, the owner, call me one time to verify a substition as she was shopping for me. The cost is the exact cost of the items, plus a delivery fee. I also tip the shopper. I believe the deliver fee is around $17. You can choose the store they shop in if you wish, and you will get the original receipt. They will also use coupons for you if they have them. I believe we have saved the delivery fee over shopping at the resort store every time.
We usually order water, juice, soda, coffee, breakfast food, fruit, cheese and crackers, snacks, beer and wine.
I always schedule a late afternoon delivery and have the groceries delivered right to my Villa. However they will deliver to Bell Services, who will store your groceries, including refrigerating perishables for you. You call for your groceries once you are in the room and of course tip the Bell Man too.
Garden Grocer is also widely used by folks on the DIS. Here you shop a "Virtual Grocery Store" and choose from their website. I believe the prices are marked up a bit, but their delivery fees are lower.
Both are reputable services with many devoted followers. It is a great solution for getting groceries delivered to WDW
HTH