I have to agree with Art on all points.
This is why I am tending to favor the 30-06 +/- class cartidges over the super magnums. Still, more speed is less drop and better BC in the bullet means less adjustment to make. That is why I am thinking the rifle that has the most recoil that you could comfortably handle would be the best choice. Which is very subjective though. Maybe some of you can sit all day and blow off 340 Weatherby rounds. I'm not one of them though.
There are lots of rounds that I think would get the job done. I think I'd stick with between a 7mm and .338 as far as caliber goes. Even if you leave out the magnums, this still leaves .280 Rem, .284 Win, 7mm-08, 7x64, .308, 30-06, 338 Fedral and a whole slew of wildcats to choose from.
In the end its probably not really all that important which one you pick even, but it is still fun to discuss.