You've had many excellent ideas posted!
We live on basically $20 a week for our family of 5. My husband is a trucker and gone most of the week, but my 3 young boys, 7 and down, eat well on the limited budget.
We do get some canned goods and a few cereals from a food bank once a month and WIC checks for one child, so that helps.
I agree with others on taking stock of what you actually have in the pantry and do "survival" cooking. You would be amazed at what you actually have in there!
Every 6 weeks or so we go to a butcher, where the meat is preservative/additive free and buy about $100 of various meats. Chops, chicken, hamburg. We freeze them in individual packets.
We check out sales and buy as much frozen veggies, canned tomatoes, pasta, potatoes, rice, eggs, garlic, onion as possible. We avoid buying any processed foods such as boxed mac & cheese and the like.
I will take 1/2 a chicken breast and cut it up into small pieces and make a stir fry or casserole so the meat lasts longer. We fill up on rice, which is a family staple, most nights. It's hard to remember, but a serving of meat is only 3 oz and we as a populace, usually eat too much.
I'll make a large meatloaf and use the left overs to make spaghetti sauce for a spaghetti feed the next night. I will make a double batch of pancakes or waffles to freeze for quick breakfasts.
Lots of recipes on the web to give you new ideas for stretching the food!
Good luck and know it is possible to eat relatively healthy on a tight budget!