A lot of great advice on this one guys. The .308 is an excellent choice all around. My choice is the 7mm-.08 with 139gr Ballistic tips. I have used the .243, .257 Roberts, 30-.06, .308, 7mm Mag, and 30-30.
The .270 and even the 260 is good cartridges. It just comes down to personal pref., but I do like the wounds that the ballistic tip delivers without a large amount of recoil. To me it the 7mm-.08 delivers an all around performance. Just my .02