Here are some of the foods that are very cheap, yet very healthy for you:
1) Oats: A big watermelon-sized bag of oats cost like 1.5 dollars, which is impressive. Oats are very nutrient dense, and in addition, they contain a lot of soluble fibre, specifically, beta-glucans that have been shown to reduce your cholesterol level as well as having other beneficial effects.
2) Beans and lentils: Beans and lentils are very cheap. A big bag of raw beans cost between 1 to 3 dollars, and you only need one scoop of raw beans to keep yourself full. They take very long to cook though, so I would recommend processing other ingredients while they are cooking. And by other ingredients, I mean:
3) Tomatoes and onions: A big bag of onions cost around 2 dollars, and the best part is, you don't have to buy organic onions at all (they have been ranked the LOWEST for pesticide residues among other vegetables) Tomatoes have slightly more pesticide residues, but they're still on the low side.
4) Broccoli: A perfect vegetable because they're a) very cheap, b) very nutrient dense, and c) very low in pesticide residues, which means you don't have to buy them organic.
5) Eggs: A dozen eggs cost around 3 dollars, and can feed you for 6 days.
6) Sardines: My favourite. A can of sardines (with 5 sardines in total) cost less than 1 dollar.
All of those above foods are low in fat and low on the glycemic index scale.