Caliber choice depends on what you already have and what else you hope to hunt with the same rifle. If you have a 30-06, I'd go with that. The 300 Win Mag is hard to beat, but it has more recoil than the -06. I wouldn't think in terms of any shot over 300 yds. That is a long shot.
As was said, 270 is considered the minimum elk caliber. The caliber choices then are between 270 and 338 for the most part. If you intend to hunt grizzly bear or any large bear with the same rifle, I would lean on the heavy side. If not, the 30-06 is good.