I handload over 60 different cartridges, but I have only killed big game with:
270 Win, 7mmRemMag, 300WinMag, 257 Roberts Ackley, 6.5-06, and 6mmBR.
I consider the 7mmRemMag 140 gr the optimum choice for a 10 pound rig with my shooting skills out to 625 yards.
If I were a better shooter or could carry a heavier rig, I would move up in cartridges and bullet weight. First stop would be 300 WinMag 150 gr.
If I were a worse shooter, or needed to go lighter, I would move down in cartridges and bullet weight. First stop would be 6.5-06 129 gr. That works very well.