We own a week at Vistana, and return often. Here is my basic packing list for kitchen stuff. I have added a couple of comments. There is an excellent Publix nearby, and a Whole Foods about 15 minutes away - my son has food allergies, so we hit both the first afternoon while waiting for checkin time.
Most items below I just pack in baggies, enough for a week because that is easier than bringing back or leaving behind large quantities. Keep in mind that we fly in, so don't bring too much. If I was driving down, I'd probably pack a few more basics in a small box.
Coffee Filters (basket type; the smallest size at Publix is 200)
Salt & Pepper (we have small ones from our camper, they usually have packets in the unit, but this is easier)
J-Cloths (2 heavy duty)
Med Plastic Bags (for storing leftovers, bringing snacks to the park)
Dishwasher Pucks (the DW deterg they provide is pretty low grade)
Laundry Detergent (Purex sheets)
Dryer Sheets
Bran Buds
Shopping Bags
Batteries
Clorox Wipes (for quick kitchen cleanups)
Hot Sauce (for EVERYTHING

)
Tuna (DW's favorite brands are hard to find)
BBQ Utensils (!)
Camp Spices
Drink Crystals (Lite/Gatorade)
Swiss Army Knife/Leatherman (makes up for any missing utensils)
Note that Vistana has charcoal BBQ's throughout the property, but they don't provide any BBQ utensils. I bought this neat hybrid tong/flipper at a dollar store.
We don't really do dishes while there either. I don't think there's anything there that doesn't go in the dishwasher. I hardly call popping the dishwasher on and unloading later "doing dishes".
One other thing for those that are used to hotels; Vistana does not provide shampoo in the baths. There is a bar of soap for the sink, and TP, but you need to bring your own shower products. I always do anyway, but others may expect them.
Note that you can also get daily housekeeping at additional cost, or included if you are booking as hotel type stay through Sheraton. If you want your bed made every day and fresh towels, you can pay for it.
Vistana really is a great resort. Have a good time!