RE: new to gun hunting
Any of the calibers mentioned above would serve you well at the ranges you suggested. The .243 might be reaching its limit at 400 yards on deer-sized game, depending on your comfort with it (otherwise, it's a great deer cartridge). Recoil-wise, the .308 family of cases(.308, 7mm-08, .260 Rem, and .243) are generally going to be less noticeable than what you might experience from the .30-06 family (.30-06, .270, and .25-06). Felt recoil also increases the heavier the bullet and/or the lighter the rifle.
But, even the recoil-sensitive should be able to handle all of them without too much difficulty. As well, nearly every manufacturer offers rifles chamberedforthem.