For the action you listed, I'd choose the 7x57. I have rifles in all the cartridges listed and although I like the 257 for deer, I don't feel it's enough gun from a bullet diameter/weight viewpoint. I've used the 7x57 on deer and coyotes(incidental to deer hunting) for over 20 years and consider it the equal of the 30/06 for medium game.
The 257 is adequate for deer and coyote and bigger game IF the shooter is careful of the application. Unfortunately, many hunters don't possess the skill or self control required to exercise this amount of care so I simply don't recommend such use.
The 6.5x55 is a good round but ammo supply is iffy unless you're a handloader and plan to buy all the brass and bullets you might ever need.
I have one that's currently in pieces awaiting an industrious period to complete the rebarrel project.