for one of my youngsters, more than a 243?

I felt very little difference in recoil between my friend's 350 Legend, my daughter's 357 Mag and my .243.

If I had to pick one for Whitetail and Black Bear it would be my daughter's Ruger 77/357. In fact it's in my truck right now as I head out Mt. Lion hunting.
Compact, lightweight and ammo is cheap and easy to find or load. With .38 Spl loads practice is pure joy and plenty enough for WT or lion out to 50 yards.