Whichever you pick, make sure you can practice with it from field positions till you can hit a vital zone sized target (say an 8 1/2" x 11" piece of paper) on demand, under time pressure, from those positions. Know how far you can do that from, and don't try to shoot farther than that.
That said, the gun with the least recoil will allow you to practice more.... I vote .270 WIN.
A military style sling will do wonders for stabilizing your rifle when there's nothing but sagebrush to rest the gun on, too:
Some people like shooting sticks, too.
Learn to use any shooting aid quickly, as well, as Ol' Donkey Ears may stop and look at you for a few seconds before he resumes bouncing into the sunset, but he won't stand there forever......