In the late l960's I discovered skirt steaks. Super cheap, and full of beef tastiness (and a raggedy texture guaranteed to keep the price down). Loved them, and this was a time when my budget needed all the help it could get. Then fajitas got invented and there went my favorite cheap steak.
More recently I've gotten into turkey wings -- very good braised. And breast of lamb (I slow cook it with spinach and eggplant).. And pork shoulder steaks - breaded and pan fried.
What are your bottom-budget secret favorite meats?