If you can't totally cut out junk foods, make them yourself. Eat out once a month and use coupons to cut costs even further. This is not as hard as it sounds. Most popular convenience foods and restaurant foods were inspired by their homemade counterparts. Ther secret to recreating these foods well is to go back to the original homemade versions.
Many basic cookbooks have wonderful recipes for homemade sauces, breads, etc.
There are some great cookbooks that strive to duplicate some of the more favorite purchased foods. One of the best is called Top Secret Recipes by Todd Wilbur. He has three books out with more in the works. Only you will know for sure what your family will miss and what it won't. Many other cultures use meat sparingly in their dishes.