One excellent piece of gear for this kind of thing is a crock pot, or you can look for a turkey roaster (a large rectangular crock pot). Then you can use dried beans, cheap cuts of meat, etc. You can also look into a pressure cooker, giant roaster pan (you know...like the black or blue speckled pan with the lid) and big soup pots. These will help you do wonderful things with cheap cheap food.
Also you want to get familiar with cheap ingredients. Shopping with the seasons is a good way to get a deal on produce, and that is mostly summer. But some things are cheap year round: green cabbage, green bell peppers, garlic, bananas, carrots, iceberg lettuce, sweet potatoes. There is also usually some variety of apple, onion, potato, squash, and tomato that is affordable. Buy your produce whole and use your trimmings (cleaned) along with your bones to make stock which will add flavor to all kinds of soups, stews, casseroles, etc. When you can't get fresh vegetables, frozen is a very nice choice. You can get big huge bags of mixed veg, peas, corn, broccoli, etc, then when you want to add a little vitamins to a dish, or when you just want to serve one or two people, you can measure by the handful and not waste anything.
Ground turkey is a good alternative to hamburger when you can't catch a sale. You can also get whole chickens, turkeys, and whole hams. Otherwise, it is best to use meat alternatives like edamame (frozen foods it is soybeans, it looks like a whole pea) also you can look for tofu, eat peanuts/peanut butter, eggs, and of course...beans! Check vegetarian and vegan websites to get your meat free complete proteins. That way you can go without meat and still get all your nutrients that ordinarily come from meat.You can get various kinds of pasta and other grains, too. All these ingredients are cheap and mix and match well for soups, casseroles, skillets, etc.
Cheap breakfasts:
Pot of oatmeal (from the round box, not the packets), scrambled eggs, homemade biscuits, banana muffins, pancakes, turkey sausage, cornbread, cornmeal mush.
Cheap lunches:
Grilled cheese sandwich, homemade soup, turkey hot dogs and mac and cheese, ramen with vegetables, tuna salad on crackers, bean burritos, or leftovers.
Cheap dinners: Pot of beans with bacon and cornbread, scalloped potatoes and ham, stuffed peppers, braised chicken thighs with lentils, spaghetti with jar sauce and ground turkey, Mexican rice with hamburger, ground turkey chili.
Cheap desserts: Rice pudding, oatmeal cookies, sugar cookies, bananas foster (no rum), cinnamon rolls, baked apples.