I hunt our SW deer with a .357, and it also serves for an occassional coyote or pig. No bears. I've used various loads, mostly handloads.

Anything you catch broadside inside 75yds can be taken down with anything from 125gr up, it seems to me. However, I prefer 158gr softpoints for the less than perfect angles, especially pigs. Expansion is nice, but penetration is vital, and I hate to have to track down crippled animals. Shot placement is key.
Compared to my .270, the .357 does not produce enough shock to matter, and the animal dies from blood loss, unless the bullet hits the spine and drops it right there. YMMV

__________________
Science plus Art