Pure lead projectile in a muzzle loader - perhaps the cheapest.
223 with a non-varmint bullet of perhaps 55 grains. I would not go with smaller than a 222 with jacketed bullets.
When I was young we could only afford cast bullets and the rifles were $10 Springfields - it worked. Any 30 caliber cartridge from 30-30 on up would work as well. With the cartridges I have on hand though I think a 375 Win with cast bullets would be my choice or perhaps my muzzle loader.
If you’re going to shoot cast, I think 30 caliber to be minimum (maybe 7mm). The larger the caliber the better to a point for effectiveness.