These may just have a freezer with some chicken and some bags of rice, or they may have a selection of canned goods. This is where people without cars shop for the basics. Don't think about the price. If it is something you usually eat, buy it. Most stores are closed on Sunday, but IGA is open until noon.
Fresh meat is difficult to find.
Most meat is frozen and the selection is limited. If you are willing to buy a case or large amount, try the Merchants Market wholesale in Little Dix village. From the airport, turn left and go straight through the intersection at Albert's and into Stoney Ground Village. In about a mle, you should see the sign for Little Dix village and find Merchants Market on the right. Case quantities of Beer, Coke, Ting and bottle water are available at Tropical Flower Wholesale for good prices.