Any caliber from 7MM-08 through the 30-06 will do for any whitetail hunting at most any range that deer should be shot at! There is not enough difference in them to raise a fuss over! Pick one you like and go with it!
Yep, what he said except that I'd start out with the 243 and go on up from there.
If bigger game might be in the mix later on then opt for .270, .280, 30-06, 7mm-08, or 308.
IMO the .270 Winchester is real hard to beat. Light recoil and very flat shooting and perfectly capable of larger animals like elk.