Eggs, being gov't subsidized, are cheap. And you can vary flavors and fillings a lot.
There are inexpensive cheeses, too.
Frozen veg are cheaper to purchase, there is less waste, and they are very close to being as nutritious as fresh.
Soups are filling -- look through the recipes section for some that would appeal to your family.
Hope these help -- my husband grew up on peanut butter and marmalade on white bread, and gross frozen fish -- the cheapest.

It is hard to eat both well and very cheaply, low-carb or not!