My husband and I like to do "bulk" shopping, and purchase mostly large-sized items. This actually works well for corn-free shopping, as we tend to buy mostly ingredient-type foods. We shop at BJ's and Whole Foods regularly to stock up. My husband also makes weekly small trips to the local Market Basket, and sometimes to Shaw's and Stop and Shop.
Are you near a Whole Foods Market? I highly recommend this store! I do the bulk of my shopping there, and buy many of the 365 brands; for example, tuna fish, bread, soda, peanut butter and spaghetti sauce. I also buy my chicken and pork there, as their meats are naturally raised, as well as safe bacon, sausage, hot dogs and kielbasa.
As always, read the ingredients before buying/eating. Bring the list with you, and when in doubt, don't bother with the food! You've probably read this elsewhere in terms of saving money at the grocery store, but make sure you shop on a full stomach. It's hard enough to be in a grocery store when you're hungry, but when you're also surrounded by foods you cannot eat--that is a very uncomfortable situation.
If possible, and if you don't have one, I suggest investing in a freezer and probably a Seal-n-Save as well. We buy huge packages of meat and then divvy them up in sealable packages, marked with the date. This makes shopping in bulk much easier. Although I often state it's not worth keeping separate foods in the house, we do keep separate meats. My husband buys conventional pork and chicken, while I can only eat the naturally-raised pork and chicken I get at Whole Foods. We label the packages, plus I keep my meat in a separate place in the freezer.