Sounds like 30:06 as Sampleman stated.
Personally, I have found RugerM77 rifles to shoot well and are reasonably priced. I hunt with a M77 Ultralight “Mountain Rifle” because I carry it more than shoot it, but at the distance you say stick with a longer barrel.
Any ultralight rifle should be limited to 250 meter shots. The thin, light barrels are prone to gross loss of accuracy due to harmonics and vibration, temperature stress and bedding mechanics.
The longer barrel theory is also incorrect. Anyone who has shot in competition, knows that the longer the bullet spends in the barrel, the more accuracy is lost due to jacket deformation.
The minute gains of velocity that a longer barrel may provide, only amounts to a few feet per second, but the effects of friction, vibration and bed mechanics, effect bullet flight to a far greater degree.