I have used the .243 Win, .270 Win, 7mm-08, and while I haven't had a .260 Rem, I do have a Howa 1500 chambered for the 6.5x55 Swedish Mauser. All of them are fine cartridges and would work well for the tasks mentioned, coyotes and deer. Obviously, the .243 is going to have the least recoil, but if you get one in a short barrel youth model, the muzzle blast might make for a greater flinch than a 22" barrel .270 Win. If the OP handloads, I would suggest the .270 Win. It can easily be loaded down to .243 Win recoil levels, and in full load version is capable of handling larger game. If the OP is not a handloader, then the .243 Win is probably the best option, just don't fall for the 16" barrel version. I don't like muzzle brakes, either, because you only get one pair of ears, and they need to last you your whole life.