A very soft lead flat point at moderate velocity.
I have been experimenting with wadcutters, both double ended and hollow based, they are super accurate. The standard double ended wadcutter penetrates well. A hollow based wadcutter loaded backwards expands very well but penetrates less, about 50% less in water jugs. A coyote shot at 75 yards with a 32 S&W long loaded with a full wadcutter dropped in his tracks. A deer shot in the lungs with a reversed 45 Colt hollow based wadcutter ran about 20 yards. Its lungs were destroyed. The recovered bullet was perfectly expanded and stopped by the hide so it was damned near a passthrough. The shot was at about 10 yards. The handgun was a six inch S&W model 25.
I have yet to kill any critters with a 38/357 wadcutter but have shot them into water jugs. A semi-wadcutter hollow point would also be an excellent option in this caliber. The low recoil of moderately loaded wadcutters aids accuracy and most likely rapid follow up shots.
The downside to these projectiles is that they are not suited to self-loaders.