I bought my mom a LCP 380 last year for christmas. She hasnt shot more than a box through it just learning how it works and what to expect, but she is very capable. The gun shoots great to be so small, but is very snappy.
My fiance carries a S&W 642 .38 special. Great gun, fool proof, cant hit the broad side of a barn more than 10 ft away.
I carry a S&W M&P Shield 9mm that shoots great.

The 642 is a great gun for beginners IMO, but i personally like having more than 5 shots, and also i like something more accurate. Her sister carries a LCR that handles well and shoots great.

The LCP is very small, can fit in my pocket. Hold 6+1, which is still not much, but gets the job done. Much more accurate that i thought. The gun is as much, or more snappy than my 9mm is.

My shield has never let me down. Goes bang every time i pull the trigger, has a flush mag that holds 7, or the extended mag that holds 8. With the extended, it has a long enough grip to get your entire hand on, as long as you dont have huge hands of course.

Sister in laws boyfriend carries a KelTec P3AT that has had multiple issues. Would not trust it with my life.

If it were me, I would buy her a M&P Shield or LC9 if she has the know how. If she has never handled a gun, the 642 or LCR is a great gun. If she needs a smaller gun, the LCP fits the bill.