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I'd go for .270, .280, .30-06, 7mm Magnum or one of the short magnums. .45-70 is going to leave you wanting more range in the mountains, scout rifle with that short barrel will as well.
I personally shoot a Remington 700 Mountain Rifle in .280 but unless you reload, I would steer you away from it. The problem is ammo availability. If you reload, you have far more choices in ammo with a .280 than you do a .270 and I'd argue its also more versatile than the .30-06. However, if you have to buy ammo for it, well you will find one box 140 grain .280 ammo at Dicks and that's it. If your stuck out in the field and forgot your ammo at home, if you have a .270 or 30-06 almost any sporting goods or country store or gas station in hunting country is going to have boxes of ammo to sell you. 99 out of 100 times they won't have .280.
You'll certainly find .7mm Mag or .308 at Wal Mart (your probably not going to find .280 there) and likely at country stores too, but even then its a hit or miss proposition where if you have a .270 or .30-06 you will have no trouble finding ammo anywhere.