Bad shoulder? I have several 270's and 308's and I would not consider them (except the 1 muzzle broke 308) light on recoil, especially for a bad shoulder. Considering that...I'd go with a .243 WIN in a youth model (WBY Vanguard is an excellent choice for the $$). Ammo options will allow one to hunt any deer in North American, are available everywhere and is inexpensive...(well inexpensive is relative in today's world). My 11 year old niece and my 7 year old daughter both hunt with 243's and handle the recoil well and have no problem taking game.