At one time I would have said 158 gr lead SWC- go for penetration. The HP rounds that were being loaded "back in the day" just did not expand at snubby velocity.
However, there are some much better loads being made for self defense today. Personally partial to Speer and Hornady, but there are other good ones as well. Check the ammo makers websites, and look for Self Defense rounds for a snubby.
the gun is a vintage smith and wessen chief special not pluse p rated but i have seen a bunch of self defence loads advaibal in regular old 38 spl im leaning tourds the Hornady rounds 125 jackeded hollow point
I have a 38. snubby, +P rating. I use Remington Golden Saber +P 125 gr HP. for carry purposes. I think for your gun, 125 gr copper jacket HP rating is fine. Do not use +P round. For target shooting, I'd suggest a 148 gr lead wad cutter round.