I just shoot and see what they do. You can only test in water and gel so much before you have to do the real thing. In all my time hunting I'm convinced of two things when it comes to calibers and hunting.
#1, Most people haven't the foggiest clue what their bullet does. A shocking number of people can't even tell you where they hit the deer beyond "hit hard", or "in the chest".
#2, Animals are not bulletproof in the slightest.
I'm not going to say you should use the absolute minimum it takes, but I think most people would be surprised how well even a 380 acp could do. What I will say is almost every discussion you see about such things either involves calibers so many times more powerful than required, and/or something to the effect of "in case of a bad shot". I don't believe there is really such a thing as overkill, and I don't want to go down the rabbit hole of bad shots.
As for 357 magnum, it really depends on the person. Some people are not happy unless they are shooting high velocity rounds like a 300 win mag, and hitting them with light bullets that are nasty on impact. Something like that will drop a deer in its tracks most of the time. If that isn't something you want, then a 357 magnum does not lack much. Bullet selection is not that important, although I wouldn't mess with the super light bullets. Most anything 140 to 200+ grains is going to do you just fine. Even hollow points are going to pass through most of the time on most animals. No it isn't going to turn organs to jelly, but it will punch a good 1/2" or bigger hole through there.