What is JHP? I have several rounds as options, including various grain 357 loads and 38 special and 38 special +P loads.
Jacketed Hollow Point
Most any 125gr HP’s will more likely expand, and thus dump more energy than the 38’s.
Jacketed Hollow points.
Just buy a box of COR-BON .357 Mag 125gr DPX. It's probably the best self-defense round you can get. There are some others and people will argue with you, shrug. If you can't find it, get some 125gr Federal Hydra-shok. The lighter grain bullets don't penetrate quite as deep as the heavier rounds(in general) but expand nicely.
My personal opinion is that I would only switch to 38sp if I had control issues shooting a .357. It really depends on your gun and your comfort level. I have a Smith and Wesson 638 that I run .38sp +p in when I carry(outside of NJ). Even with the small 2inch barrel, control is trivial. That said, I've shot the .357 version of the same gun and it takes quite a bit more effort to keep the on target. Still doable, just more difficult.
There's my advice...get some Cor-bons load 'em and forget about it, you're good to go. Definitely keep to 125gr or smaller.
JHP=Jacketed Hollow Point.