Our staples are chicken, which can often be found for $ 0.50 - 0.60/lb (frozen quarters), and beef heart which is around a dollar/lb depending on where you get it. Then I stock up when other things are on sale, like pork, turkey, or lamb. Sometimes I get them a duck or cornish game hens.
It helps to have one or more large freezers so you can stock up when things are on sale. I've been known to buy 200 lbs of chicken, turkey, pork ribs, etc. when it's on sale
If you have small farms close by, and they have their animals butchered at home, they will usually give you things like kidneys, liver, pancreas, tripe, lungs, hearts, etc. for free. Also if you call the butcher, he might have tons of that stuff that he'll give you. The old butcher used to give a lot of it to us, but the new one is afraid to get sued ( in case a dog gets sick) so he just throws it all away
I have a couple of farmers that will call me anytime they have animals butchered, and I'll come out and pick up pretty much everything they don't want.