1. A comprehensive reference cookbook for when you need to look up what temperature the oven needs to be to roast a chicken, how to make pie dough, what water:grain ratios are for cooking different grains, etc. I use Joy of Cooking for this purpose, but there are others that could fill this role.
2. Mennonite cookbooks (More with Less, Extending the Table, and Simply in Season) - as well as recipes these have lots of discussion on saving money on food and eating in season.
3. Moosewood cookbook, Mollie Katzen - While not specifically a budget cookbook, many recipes are affordable by virtue of being vegetarian. The Moosewood cookbooks also do a good job of incorporating international flavors without calling for obscure ingredients.
4. Wild Fermentation, Sandor Ellix Katz - A fermenting book. Lots of excellent recipes to make things like saurkraut, bread, and pickles from scratch. Also, since fermenting helps the food keep longer, possibly a good way to use garden surpluses so they don't go to waste.