Id go with the tried and true 30-30. Low recoil still enough for deer and available ammo all over the place. My other picks would be 30-06 and 308.
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