If you don't already have a firm grasp for sound nutrition, getting those basics down pat is a great place to start. Dollars are spent on food items that offer very little nutritional value to the consumer, which is a big waste of money.
Processed/convenience foods, while often fairly inexpensive, are usually poor choices nutritionally, and should be left on the shelf.
Fresh food, including grains, meats, veggies, fruit, and dairy provide nutrition, and when you prepare your meals, you control the amount of salt and fat, etc. that goes into the meal.
Grains----oatmeal and other whole grain hot cereals are inexpensive per serving, provide bulk for a healthy digestive system, crude protein, and many vitamins and minerals. Avoid cold cereal.
Meat should always be limited to 3-4 ounces---one of your most expensive components is offset by reducing serving size.
you have discovered chicken thighs. Buy meat on sale and fill your freezer. I always cruise the mark-down section in the meat case and find great deals.
Pork is quite reasonably priced most of the time. Fish from the freezer case (plain fish fillets) is usually reasonably priced compared to the fresh fish on ice.
Beef cuts, such a london Broil, are fairly inexpensive, have little waste, and once marinated and grilled can be made into lots of different things--sliced thin and used in sandwiches, salad, burritos, soup, etc. So one purchase can feed you for several meals. Avoid lunch meats.
Eggs are cheap and a great protein source
Cheese, while expensive, is nutritious and delicious, and an ounce or 2 is a serving---so a big brick will last a long time.
Pasta---always inexpensive, filling, and nutritious. Very versatile, too.
Fresh produce is nutritious. Buy fresh fruit rather than juice.
Milk, while more expensive than it used to be, is nutritious, and still cheap compared to the number of servings/gallon.
Prepare your own meals with fresh ingredients. It will pay you back in many ways.