I am not sure about the grocery stop as I have never made use of them, but there are several towncar services that provide transportation to and from the airport.
I have used Tiffany Town car in the past and have had good experiences with them, but I am using Cartier Town car this trip because they were $15.00 cheaper.
FL Tours is a sponsor of the boards and they have gotten good reviews, they do not accept credit cards though, other people have used YourRide as well.
The cost for a town car runs $75 to $90 round trip depending on what company you use and which resort you are going to. Going to the MK resorts is usually the highest cost.
Mears is a shuttle service that is cheaper but they go to various resorts dropping off several passengers. The town car service is nice because they pick you up and take you directly to your resort.