There are a whole lot of good chamberings for long range shooting mentioned by the guys above.
In 1957, I had my first custom rifle built. It was a 7mm Ackley Magnum. That was prior to the 7mm Remington Magunum making the scene. PO Ackley built the rifle for me. That was the ONLY rifle I owned at the time and I used it for everything. I shot 160 and 175 grain loads with it and made some very long groundhog shots with it back in my home state of Pennsylvania.
I know for sure that many of the chamberings mentioned here will do what you want. But, I'm just a 7mm guy. I have a heavy barreled 284, a 7mm Rem Mag, and two 7x57's all shooting the 100, 110 and 120 grain bullets accurately enough for long range varmints. Just last week, I tested some 100 and 110 grain loads in my new 7x57 with a Shilen barrel that shot three shots into less than 1/2" groups at 100 yards; the 100 grain Sierra HP and the 110 Speer, both excellent bullets. The rifle is a new Rem 700 CDL that the gunsmith removed the factory barrel and installed a Shilen, 24" barrel with the same taper as the factory barrel so it fit the stock well. The rifle without scope weighs 7 pounds, and balances perfectly. I LOVE that CDL stock and it fits me perfectly.
Martyn