Turkey pieces can be fairly cheap, but another good choice is fish. Basa [aka River Cobber] Coley, Dabs and Pollack are good 'budget' types of fish, or if you like a dark flesh/oily fish, then mackerel. If you live near the sea and there is a fishing fleet near you, there is a chance you may be able to buy directly from the fishermen, you can at Hastings which is about 2 miles from me, and there are several fishermen's kiosks where they sell fish which is good to eat but does not get to the general market. If you live away from the sea, most supermarkets have a fish counter and frozen is often cheaper than fresh,this assumes you have a freezer to store it in..
Other than fish, another good choice is liver. You could continue with chicken, but legs ['drumsticks'], thighs or wings are usually cheaper than breasts. Aswith fish, you may find frozen cheaper than fresh.
I am assuming you live in GB, if you live anywhere else, some of the information I have given may not apply.