I agree with lots of the others and would like to add a few things.
Beans- black, white, pinto, split peas, butter, garbanzo- etc
Rice- you can buy 10lbs for around $4.
Potatoes- you can find 50# sacks for about $10 certain times of the year from local grocers and Save-A-Lot stores.
Pasta- consider buying in bulk at a Cash-n-Carry or at Sam's, Costcos, or other local retailer.
But what is on sale- lately, it's been chicken cuts at .99 per pound.
Oats- cheap, healthy, and one barrel could do you both for 2 weeks at about $2.50 to $3 for breakfast.
Eggs- our Aldi has them for .49 a dozen. A perfect food! Fried go further for breakfast. Use them for a main dish as in the case of strata, quiche, and frittata.
Onions- they run on sale at 3lbs for .99. Very healthy and very cheap. Make onion soup, finely chop to add to ground meat to stretch. (By adding ground veggies and bread crumbs, I can stretch one pound of meat to make 8 patties!)
Carrots and sweet potatoes when they are on sale- I grouped these together because they can be used in a similar manner. Boil, drain, add a dab or butter and honey or molasses. Mash if you like. Shred in your ground meatloaves and patties or baked meat dishes such as Enchilada Bake. Roast with butter and parsley.
Celery- cheap and you can stretch soups, ground meats, and eat raw.
Cabbage- cheap, good for any soup, use rice and a little ground meat in cabbage rolls. Goes very far as slaw!
Bulk, sales, and outlet type stores (such as bread, or dented can outlets and the like) are great places to find cheap food.
Learn to can and freeze when you buy in bulk. Always take any food that is given to you. Save all scraps in the freezers for casseroles and soups. Boil bones from chicken etc for a healthy broth. Buy turkeys when they are on sale in November. One could last you two for 14 meals.
Check out momsfrugal.blogspot and ThePrudentHomemaker. The PH feeds a family of 8 for less than $3 a day! She has some very very good ideas! Blessings to you both!