There is a lot to be said for having "one gun", and sticking with it. If you can get it to shoot, it helps when you have the confidence in the gun.
To carry the same gun in September for Antelope, October for Mule Deer, November for Elk and Whitetail is a good way to remove one more variable from the equation. Always, the biggest one you can shoot accurately, unless you some unique set of circumstances, like Sheep hunting, or something where the lightest gun is required.
And then, no matter what gun you have, go spend an equal amount on the Scope.
I think I would have to agree on the one gun theory. I am just weak and keep buying more. I take at least 3 rifles with me to elk camp. The last thing I want to do is go home for another rifle should something break or come loose. Laat year in the middle of my hunt, a screw from my trigger guard came out so I just grabbe another rifle.