ORIGINAL: ShatoDavis
If your recoil sensitive You shouldn't choose any of the magnums. My suggestion would be to purchase a 280 rem it would be perfect for what you described Its in between the 7mm-08 and 7mag in preformance. The 280 is more than adequate for elk/Moose/caribou etc. with premium 140 gr.+ bullets;and its an awesome deer round. Another fine choice would be the venerable ole 30-06 though the 280 gives slightly better trajectory with less recoil IMHO. With a good Limbsaver pad the 280 is a pleasure to shoot.
Agreed, you wouldn't need to save or buy a deer rifle as the 280 rem would fit the bill nicely their as well. Though if leaning towards a 7mm 08 purchase the 280 rem also use the same .284 bullets so that would allow you do the same as with the 7mm rem mag without the extra report.
I myself use a 7mm rem mag for upto Mooseand find tolerable with a bummed shoulder. I have a Pachmyer Decel Pad on wood stock 700 action, to my shoulder it feels less then my partners 280 rem abolt medallion. His gun is smaller/lighter, factory padand doesn't fit me worth a hoot, no doubt the main reason why I feel it more. Weight and fit of the rifle does make a difference in regards to felt recoil. The aftermarket poads also do help a lot in this area as well.
The 7mm rem mag would certainly do nicely as well but apples to apples in rifle styles/models will recoil sharper& more muzzle blast then the 280.