My advice would be to buy frozen if you are on a really tight budget. Buy seasonal fruits and veggies when buying fresh. Skip the fancy packaging and pre-cut stuff. When you get home you can chop up a head of lettuce and put it in separate containers for lunch. Research online for 'how to store produce.' There are an excellent infographic going around online from a mom & pop grocer with the idea location and shelf life of practically every western fruit or vegetable imaginable. It's definitely possible to eat healthy on a budget. You can order your dry goods online or buy from a discount store like Big Lots to save a little more.
Beans! Beans are super good for you, they have lots of protein and are high in fiber! The best part is that they're really cheap! You can find them in any grocery store. You can literally make anything with beans. Soup, salad, dip, even burgers!
The best thing I found to eat healthy on a budget was to purchase single fruit and veggies instead of prepackaged. I can purchase a better variety and spend just as much or less. I also purchase meats, poultry, and Fish the same way. The store I shop offers a meat, poultry, fish cases, that I can purchase any quantity I need. Again, this allows me to buy just what I need, no bulk, no waste, less spent. The store I go to offers organic choices, too.
As for meats, stick with cheap stuff like pork and dark meat chicken. You can do red meat too, but just look for roasts that are on sale for buy one get one free. You can cut those up into a ton of portions -thin steaks, cubed for stews, even grind some if you have a meat grinder. For chickens, get into the habit of buying whole or minimally processed chickens and breaking them down yourself. Black beans and rice form a complete protein from what I've read. Buying both dried as opposed to canned or parboiled will also save you a lot. One of my favorite things to make is a simple beans and rice - I make the rice with chicken stock and my favorite jarred salsa, along with a few dashes of cumin, then just prepare the black beans according to the directions and mix them in with the rice. You can even save on the chicken stock by going with a good brand of chicken base instead, such as Better Than Bouillon brand chicken base. This is a great filling for burritos with a little shredded cheddar, you don't even need to add any meat.
This is an excellent suggestion, particularly because meat has turned into a expensive item lately and it's necessary stretch it as much as possible, and this is the best way to get this done.
Personally, I would find a local farmer rather than buying your food from a grocery store where your produce is smothered in pesticides and less than half the size of what you get from a farmer. You'll have to eat seasonal foods, but they're amazing, clean and HUGE. Once you're a clean eater, you won't be eating as much (it's harder to feel full on synthetic foods) and the food will give you more for your dollar, so in the long run, if you don't compare specific foods but your BILLS instead.. it's cheaper to eat right. Has been for me anyway.