+1 on the 165-gr Gameking.
What do you need to be shooting any bullet at 3,000 fps at game closer than 200 yards?
These bullets are designed to expand at an impact velocity of 1,800 to 2,400 fps. They are great in a .308 at 200 to 300 yards, or a .30-06 at 300 to 500 yards.
I have a dozen .30-06s, that shoot all these well: the Sierra GK, the various Hornadys, Speer, Nosler... Some will drive them at 3,000 FPS. The fellow who bought my Tikka T3 Lite SS in .30-06 has used it to kill a half dozen elk and a dozen big mule deer, at ranges of 200 to 300 yards, with Sierra and Hornady 165 GK and the Hornady 180-gr SST. They aren't intended for shooting 100-lb deer at 100 yards.