Any of those cartridges are fine for elk. The most important thing is finding a rifle that fits you well. This makes it easier & more pleasant to shoot, so then you'll practice more, and then you'll be far more likely to hit where you're aiming.
'taint the BOOM that kills 'em, it's the holes & the broken body parts!
I'm taking my 7x57 (just an old-school 7mm-08) to elk camp this Fall. The hunters may laugh at me, but the elk won't.
Good Luck!
FC