First of all, to be successful cooking on a budget, you must want to cook and enjoy the process of preparing meals for your family.
With that said, let's go shopping. We want a well stocked pantry with staples that we can call on when we need them. Things like dried beans, pasta, flour, sugar vegetable oil or olive oil, cans of whole peeled tomatoes, tomato sauce, tomato paste. Buy meats on special and put in the freezer. Look for frozen veggies on special as well. Don't buy pre-prepared foods. Buy as basic as you can.