Did you look at the Ruger Scout series?
It's bolt action & comes in 7.62mm(.308).
The 7.62mm is a good all around caliber for the game you plan to hunt.
I like the new .300AAC Blackout round too.
Online reports & reviews say the .300AAC Blackout was R&Ded for sound surpressors/spec ops marksmen but it has good ballistics.
The 6.8x40mm(6.8SPC) has merit but it's not really as popular as a 30/06 or 7.62mm.
I'm not real familiar with the Savage Arms rifles. Id get a Remington, Weatherby, Winchester, or Ruger first.
www.Ruger.com www.gunsamerica.com www.gunsinternational.com