If you are shooting bench rest at silhouettes 500yds or less the .308 would be a good choice. At extreme distance the .338 Lapua has proven itself and holds the record for longest confirmed kill. Just get you pocket book ready for the gun and ammo.
When I was looking for similar I decided on .308
If it was good enough for the Marine Sniper Rifles for so many years I figured it was good enough for me.