Buy whole chickens and make that meat work for you. A 4-5 pound roaster will feed 3 people with some to spare plus all the bones and meat scrap to make soup for around $8. Learn to break the chickens down efficiently to give you more options of how to cook it. Cook up plain, white rice with some carrots, celery, onion and a bit of the chicken stock you made from the bones before you finish your soup and season it with salt and pepper. Frozen vegetables are fine, and in-season, fresh vegetables are generally inexpensive. You can feed 3 people for about $11-12 and have a small pot of soup for lunch the next day.

Same principles apply to turkey...