I keep the Hornady 110 gr FTX Critical Defense in my J-frame .38 as per the results on the Lucky Gunner tests. I normally use a .380 ACP for pocket carry nowadays but my J-frame is still my backup.
Another strong contender that isn't on the Lucky Gunner chart is the Underwood 158 Grain Lead Semi-Wadcutter Hollow Point. This is a modern version of the old "FBI load" that was more popular decades ago when cops carried revolvers. I wouldn't recommend this to a female shooter, though, because the recoil is noticeably more than any other standard pressure .38 round I have fired through my revolver. Although I am very confident in the lethal effects of these rounds, I prefer the Hornady Critical Defense for easier recoil management.
I'm pretty sure I have seen Paul Harrell test both of these on meat targets in one or another of his .38 for self-defense videos.
I also second that for an inexperienced female shooter, she really needs the range time, and may also need some larger and softer grips installed, to help master shooting a S&W revolver. Between the DA trigger and the recoil on these guns, they are not easy to become proficient with, especially with that skinny wooden grip. I run a Pachmayr Diamond Pro grip on mine, and it makes a huge difference in the shootability. You can actually go to the range and have an enjoyable time shooting it. It adds bulk which may hinder concealment, but for a nightstand gun I would strongly recommend it.