I only shoot 4 different bullets so my choices will reflect those.
For Coyotes: Smallest I use is a 17HMR, biggest 45/70
For Deer: Smallest 357 magnum biggest 45/70
For elk: smallest 45/70 Biggest 45/70
For Bear: 45/70
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