my brother has a 77/357. For him the Winchester White box 110 grain was the most accurate but its too light (both bullet and velocity) for deer.
Shot placement is everything! I would rather take a round of 50BMG to the foot than a 22short to the base of the skull.
all 25 of my guns are 45/70 govt, 357 mag, 22 or 12 ga... I believe in keeping it simple