Personally, I like Publix, but there is also a relatively new Albertsons that is very convenient as well. These directions all hinge on following the South Exit from the airport, taking 417 to WDW. Please note that there will be 2 toll plazas, with $1 tolls at each.
From the terminals, follow the signs for the South Exit. This will put you on 417 toward WDW.
To get to Albertsons, head down 417 to the exit for Orange Blossom Trail (17/92/441). There may be a toll plaza at this exit - if so, it will be $0.25. Off the exit ramp, turn right onto Orange Blossom Trail and the Albertsons will be in the shopping plaza on the right. You will see the shopping plaza from the highway. Albertsons has a preferred customer card so take the time to fill out the paperwork for additional savings. When leaving the store, turn left onto Orange Blossom Trail and get back on the 417 toward WDW. Again, there may be a $0.25 toll as you get back onto the highway. Take exit 6 (Epcot/Downtown Disney) and continue straight off the exit ramp onto WDW property. Stay in the left lane and follow the signs to the MK resort area. There is also a SuperTarget on Orange Blossom Trail on the other side of 417.
To get to Publix, continue on 417 to exit 6 for Epcot/Downtown Disney. The exit ramp will put you onto SR-536. Stay to the left and at what I think is the 2nd light, turn left onto SR-535. Continue on SR-535 approx 2 miles. You will pass an area of hotels called Calypso Cay (there is an Amerisuites among other hotels there) on the right and shortly after that, you will make a left at a light into the Publix Shopping center which is just before you get to 192. To get to the WL from here, turn right onto SR-535 and proceed back to SR-536. Turn left onto SR-536, stay in the left lane onto WDW property and follow the signs for the MK resort area.
