A lot depends on how much recoil you can handle. For elk and moose one of the 30 caliber magnums would be good if you're going to hunt them where there could be a long shot. But they are a bit much for deer and could ruin a lot of meat. You do say 150 to 200 yards though so I'd say go with the tried and true 30'06. It's powerful enough for any moose or elk that ever walked out to those ranges, most are very accurate and recoil won't be too much for most people. It's been around for over 100 years so it must be doing something right!
"An unarmed man can only flee from evil, but evil is not overcome by fleeing from it"
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i would suggest something along the lines of a 30-06 or maybe even the 7mm Rem. Mag. or even a 300 Win. Mag. any of these will do nicely. the 30-06 will have way more factory ammo selection available, but if you reload, you can load up ammo for the other two not available in factory loads.