I’d concur with the 308. I’m fond of the 7-08 but ammo can be tough to come by. 308 will serve you well.
It’s the end of deer season. You didn’t mention your budget, but I’d strongly suggest you consider the used market. A used Remington 700ADL or Remington 788 should fit any budget and, with their short actions, provide you with just what you’re looking for.
Folks are fascinated with new guns and many will be dumping their older rifles. Take advantage of that and get an excellent rifle at a good price.