For healthy and cheap look for canned and frozen INGREDIENTS. Don't go for canned/frozen finished products. Stick to that rule and you'll have healthy food at little cost. Stay away from fresh items at this point. They tend to be pricey, time consuming to prepare, and people tend to let them rot meaning you lose your money. The main exception for me is that I like fresh onion/garlic since that is cheap and lasts a month or longer. But even garlic can be bought in a jar prechopped.
Canned fruit can be $1 for a good snack or $2 for a meal.
Canned corn/veggies are delicious with a dab of butter and salt/pepper. Should be $1 for a snack or $2 for a meal.
Frozen veggies are quick, simple, and cheap. Microwave them with a dab of butter and salt/pepper. Or put them in boiling water and add noodles all together and 6-10 minutes later your meal is done.
Then learn to prepare a few simple items in bulk that you can freeze. Pour a can of diced tomatoes, a small can of tomato sauce, a small chopped onion, a spoonful of chopped garlic, and whatever spices you like and let them simmer. I suggest lots of salt, basil, oregano, and hot red pepper for spices. There you have the best spaghetti sauce or pizza sauce you'll ever have (for pizza go with more oregano and add olives/red bell peppers, for spaghetti sauce add basil and mushrooms/green bell peppers and a splash of alcohol if you have it). Make it 10 times that size and freeze in quart bags or sealable plastic containers. Now whenever you want it, microwave a frozen container and boil some noodles and 10 minutes later you have healthy and cheap spaghetti. For pizza, use any form of starch (bread, tortillia, english muffin, or pizza crust) add sause and cheese. Each meal can be under $1 ($2 if you eat big).