I subsist very well on a very low food budget already (other than drinking, going out, etc. though that'll go out the window once I start 1L).
The Staples -
1. Dried beans in bulk. A pound of dried black beans is around $1, cooked up it makes ~3 lbs. Same for chickpeas, lentils, pinto beans, great northerns, etc. Incredibly cheap, high in protein, iron, and fiber.
2. Bulk bin shopping at health food stores of rolled oats and brown rice. Each are like $0.75 a lb and you can stock up on those easily.
3. Large bulk bags of fruits and veggies from Costco. $7 for 5 lbs of broccoli, cauliflower, blueberries, peas, etc.
Actual Groceries -
The only real fresh groceries I don't buy in bulk are really cheap anyways. Big bags of onions and potatoes you can store easily and they last for a long time. Carrots are like $0.60 a lb, Kale is $1 a lb, bananas are $0.40. The only real splurges on the grocery bill of mine are natural peanut butter and nice whole wheat bread, which even then aren't really expensive. Meat will really drive your prices up, but since I'm a vegan it doesn't matter to me. Dried legumes are going to be a lot cheaper for you.
All in all, I think I spend about $75 on groceries every 2-3 weeks.