There's more than three affordable animals lmao. Even if you count fish as one you still have crawfish, shrimp, fish, beef, chicken, pork, lamb, venison, turkey, etc. This also doesn't even account for the million ways to prepare the meats
I hunt, so no need to worry about buying, but Broken Arrow Ranch sells wild venison and boar, and I'm pretty sure they ship nationwide from their website.
Never count fish as one! That's such a disservice to fish. Salmon, tuna, red snapper, swordfish, catfish, they are all delicious in their own way and have unique textures. And don't forget scallops and other delicious mollusks!