Have her be an active involved participant in this decision, instead of just "my ol lady dun neid her a pistal"
Regardless of the gun that she goes with consistent focused practice is needed.

442/642 & LCR are the go to options in snubnose.
One MAJOR downside of a snubnose is capacity, people dont fall over from a single hit usually and criminals move in 2s and 3s normally.
Glock 42, Sig 238 and LCP are the go to options in .380.
A friend of mine carries are a 238 and absolutely loves hers.
M&P safetlyless Shield, XDS, Glock 43, Sig 938 are good options for 9MM.

I would stay away from .40 because from a small gun it can be exceptionally snappy.

If she is capable of shooting a 9MM comfortably that is the best solution for capacity and ammo costs/availability.
Look at the cost of 100rds of range ammo 38 special,380 VS 9MM.
About a $10ish per 100rds difference.