My special deer bullet for Nevada Mule deer, was the old Speer 160 gr jacked lead tip FN bullet..
That was a great bullet, and I wish they still made it. There was a 146 gr HP version as well. Soft lead for expansion, 3/4 jacket = no leading, SWC shape even if it didn't expand. I cast my own version of it, SWC solid or HP, gas checked, somewhat softer alloy, (about 50/50 wheel weights to pure lead, very scientific).
I've only killed two deer with a .357, both with 173 grain Keith 429358 bullets, cast of wheelweights, so I am sure they did not expand. Did not recover either one, but both deer (~125# on the hoof Alabama whitetails) dropped within 25 yards. I have to say I was surprised that hard bullet put them down that quickly, but to borrow from Elmer's book title, "Hell, I Was There."
I have no reservations with a good .357 gun and load for deer at close ranges, but I prefer a heavy bullet that will be likely to expand some, hence my newer . 357 bullet mold. I will carry my old 6" pre-27 or old model Ruger flattop .357s at times because I just like them and they feel right, even though I've a safe full of .44s that I suppose are technically " better" killers (but dead is still dead, right?)
Of the options you mentioned, I'd pick the 158 soft points.