You just can't go wrong with the .270 or 30-06. The 7mm mag and .300 win mag are good to, you'll kill your game just as dead, but at more of a cost to your shoulder and pocket book. If you think you're going to go after elk or bigger game at some point, then maybe you'll want to consider one of the magnums, but personally, I wouldn't. Many mule deer and elk have fallen to the .270 and 30-06. It's not the caliber so much as the shooter.
I was faced with the same decision as you, many years ago, and went with a Remington BDL in .270. I don't regret it one bit. 25+ deer, various hogs, turkeys, varmints, etc. have fallen to it, and never do I wish I'd have gotten a different caliber. Lately I've been shooting Hornady Light Magnums out of it. 140 grains, leaving the muzzle at 3100fps. I think I've shot 5 deer the last few years with it, and none of them went more than a foot or two.
Of course, there's a LOT of cartridges in that class that will do what you want. .308, .280 Remington, .270 wthby mag, .270 wsm, 25-06, just too many to mention. I looked at them all at the time when I chose, and, again, the .270 Winchester has never let me down.