The 338 is a popular caliber in north Idaho for elk and bear.My friends use them and I am considering buying one. They are especialy good for long range because they pack a hard punch with large bullets.You have to remember your in colorado and the deer there and west of there are a different species of white tail and significantly larger than whats east of there in the usa.The mule deer get as large as tule elk. Your going to be hunting rosevelts and olympics horse size animals like I hunt.The 338 is perfect for them and if you dont try to heart and lung the deer with them you wont ruin the meat.
If you plan to hunt with in 500 yard shots the old 30-06 like said above is the best caliber you can get. They dont tear up meat on close range shots and are great for bear as well.For elk I would stay at 180 grain bullets. If you dont reload the 30-06 is going to be way cheaper for ammo and easier to find not that 338 is hard to find just 30-06 is every where and usualy on sale somewhere.
The 308 is balisticly very close and is also a very common caliber and widely used like the 30-06.So it is also a good choice.The 7mm magnum and 300 winchester magnum are very good very flat shooting calibers for long range shooting.But there high velocity loads are realy tough on elk and deer and moose at closer ranges and not a good choice unless you plan to do your hunting long range. | 
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