I'd want to stay with a "short action" , so that leaves out 270, 280 ect.... I'd like to see something one knotch bigger than a 6mm bullet too, so my choises would be in this order, 260, 257 Roberts, 7-08.
260 will be all she needs with low recoil. The 257 Rbts is also good, but with less recoil than the 7-08. The 7-08 will have the most power, but also the most recoil of the three.
Most important of all, is to be sure to match the bullet design and weight to the intended animial your hunting!!!!
Drilling Man