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Depends on what you are going to use the rifle to hunt.
300 will have a pretty stiff kick and is not necessary for most North American game. I would use it for elk.
7mm will kick a bit less than the 300, also good for elk, black bears and any deer.
270 will kick the least and is ok for elk and any deer or black bear this caliber has adequate power for just about anything you would want to hunt.

Of the three choices given I would get the 270.

Given my choice I would pick the .257, I live out west and from time to time have long range shots on antelope deer or coyotes. Right now I use a 25-06 and it works great.

I' d go with the 300 but I shoot a 30-378 and love it.

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With elk in the picture I would go with the 300.

Hell, be a man and get the 340 Weatherby.

I would go with the 300 Wby. Mag. due to its versatility for yourself, but I do love my 340 Wby. Mag. Good luck.

Since you' ll be hunting out west go with the 7mm good for all big game in North America except, large bears. The 300 is good also but, has extra kick that can be avoided with the 7mm.

I would go either 7 wthby or 270 wthby and never look back...