I find the king of cheap animal protein to be pork. Leaving out arguments about taste, quality and morality of battery raised meat animals for the moment, my local Kroger frequently sells pork tenderloins on sale as BOGO (buy one get one) with a net cost of $2.49/lb. Though of course, I avoid all the pre-seasoned options.
Pork tenderloin is so lean that it needs to be cooked carefully lest it become dry, but it is neutral enough to be used in most dishes, and accepts a wide variety of additional flavors.
Center cut pork chops, if properly trimmed, as also pretty cheap - though cost, leanness and flavor vary depending on the breed and provider. I’ve had several nice duroc pork chops for less than half the cost of beef.
I’d probably look askance at most of the ground pork options, because while cheap, they run from really fatty (often sold as a sausage base) to pretty fatty (an 80/20 blend similar to a juicy hamburger option).
If I wanted a low-fat ground protein, I’d probably look at ground turkey. It’s not my favorite, and it’s not as cheap as I’d like, but it’s more reasonable than beef, and my local store has a wide variety of fat percentages, as low as 97/3 last I checked. I prefer ground chicken for the applications you mention (more neutral in flavor) but it tends to be more pricey.
And of course, there are plenty of options using crumbled firm tofu that my wife enjoys at very reasonable costs. Rather than buying “cutlet” style tofu, she’ll get a box of firm or extra firm tofu, slice it, drain it with some pressure, and then freeze it. After freezing and thawing, you’ll drop even more moisture and it’ll be very easy to crumble.
Best of luck with whatever option works best for you!