For out to 750 yards, I would easily go with .308, .243, .280, .30-06 and the .25-06. All but the .280 really a common cartridge. And the .280 kind of. (For me, the .280 lets me into the 7mm class). You could even consider the 7mm-08 or .270.
No reason IMO to go to a magnum unless you are getting into dangerous alaska big game.
But I DO know from experience, anything past 300 (and even 250 yards) takes practice. A lot of it. Reading wind, mirage, slope etc. It also takes building experience enough to know how to dope your rifle.
Rip does some wonderful things from what I see teaching a CMP rifle clinic and the Appleseed what I know of it is right there with it. Either of those would do you wonders if you want to get into medium to long range hunting.
Myself, I have .243, .308, .30-06 and .223's If I can't do what I want with one of those calibers, I don't know what will do it.