Beans, lentils and dried peas are a cheap, healthy base to build on. Soups, chili, lentil sloppy joe's, salads, and burritos are a few of the meals you can make with them. I would add brown rice next, oats, peanut butter, potatoes, onions, and then whatever veggies and fruits are in season. Right now squash and apples are in season and cheap.
Avoiding the processed crap is a lot cheaper and healthier. As a long-time vegetarian, I can tell you that eating healthy can be done on a limited budget if you eat a whole foods plant-based diet.