I would agree with the .300 Mag recommendation. You should try to find someone who has one and shoot it first, though. The recoil is too much for quite a few folks. If you are one of those folks, just admit it and look into something smaller. 7MM Magnums are real popular out here. A .270 WSM with a Nosler Accubond bullet will drop an elk reliably without a lot of recoil. If your shots are going to be within 300 yards, there are a number of mild recoiling calibers based on the .308 Winchester case that will do the job just fine - with good bullets and good shot placement. The 7MM-08 is a real sleeper with a 140 Accubond or a 150 Scirocco.