Best Rifle, value wise, for big game? (say white tail deer, mule deer, big horned sheep, elk, moose, black bear, etc)
Bolt action rifle from one of the big makers, Winchester, Remington, Savage, Ruger, Browning. Winchester guns are going up in price due to dropping availability, so unless you are a collector you are out.
I think of the remaining (hell, even with winchesters back in the running) Remington 700 boltaction is the BEST, but Savage makes a very good gun with an excellent trigger for enough less money, that dollar for dollar, Savage boltaction would be what I chose.
Now, for the average male adult, I'd pair the Savage boltgun up with 30-06 chambering.