My choice is a 7mm and probably in 7mm WSM
The reason is simple: the 7mm is the biggest caliber which has a manageable recoil for sustained firing. Secondly, the 7mm 180 grain Berger VLD is the most ballisticaly efficient bullet (BC near 0.7) without being over powered.
I shoot a 7mm STW and get 3050 fps with the 180 gr VLDs (27 ½ inch barrel) but a 7mmWSM will get you near 2900 fps which is still fine for 1000 m (1100 yds) A friend of mine came up with a wildcat based on the 270 WSM necked up to 7mm. Two reasons: 1-he wanted a 7mm and 2-the 270 case gives him .050 extra neck length which is good to hold the extra long 180 VLDs.
If 6.5mm has enough punch for you (sniper rifle) then a 260 Rem is plenty strong. I get 2950 fps from the 139 gr Lapuas in my 30 inch Broughton. I have shot it at 900m with great success. It has a definite advantage on the 308 for wind bucking and flat trajectory.