Gee, I dunno! A .243 Win for sheep? I've heard with all that armour thick hide they've got that the only bullet that'll do the job reliably on sheep is the .570 T-Rex! Only a tiny bit of recoil to get used to...
Seriously, a .223 would do the job on sheep, they practically roll over and die if you look at them in a mean way! If you're choosing a bullet, get one that expands quickly and well, no bonded stuff required with sheep!