To balance what you want in target, and hunting, I went with a 20 inch varmit profiled remington 308. It is now on its second barrel, but it was originally(and still pretty much) a remington 700 LTR. It is not the ideal hunting rifle because of its weight, and not the idea benchrest rig as its barrel is too short/not heavy enough, but I think it is a really good compromise.
Look for models marketed as varmit, or tactical, and have a 20 inch barrel. These will have a heavy barrel to dissipate heat in long string practice, and stiffen the barrel for better repeatability. These include the 20 inch tikka tactical, the remington SPS tactical, remington LTR, etc.
Like Obtunded said, the 6.5x55 would be an excelent choice. There are not many offerings in it though. Next to it, the 308 is probably what you want.