Lots of rounds will work for tender shoulders..

One that I've been playing with for a couple of years is the 25 Creedmoor.. Only one reason I prefer it to the 6.5 or 6 for hunting, that is the 100 Nosler Ballistic Tip.
This bullet in the .25 is an outstanding killer of whitetails and similar sized game.. I have killed countless coyotes and maybe a dozen deer in different locations with this set up.. I really good velocities and accuracy using Lapua brass.. Just another fine option ....