I am going through this right now. First gun show suggested an LCR in .38, and she loved the way it fit in her hand opposed to some other things.
The Taurus Poly felt cobbled together, and the Smith cost too much.
That being said, I felt like the recoil of the LCR .38 with +P was going to turn her away from actual being proficient with it. So I started looking at the .357, not because it was more powerful but because it weighed 4 more oz. I figured I could start her on standard .38s and work our way up the power scale until we found the AMMO that fit her best. And .38s are affordable due to the tupperware worship that permeates the current gun buyer climate.
Now somewhere along this journey, budget came into play. And I realized that what she needed was training and confidence. She's an accomplished hunter and all she really needs is to be shown how a semi-auto operates, and let her shoot it a couple of hundred times.
So I borrowed a Walther P-22 and a couple of boxes of minimags, and she enrolled in her CHP training course.
I also showed her the Ruger SR22, and at $299+tax it's cheaper than almost every other quality option we have looked at. And doesn't have that stupid slide-mounted safety that the Germans are in love with evidently.
If she decides to keep the Ruger in her purse, I will load it up with Velocitors, and won't worry about it. If she can put 8 in the 10x ring and 2 in the noggin, it's good enough RIGHT NOW. It's a gun the whole family (including kids) can enjoy at a very affordable price point and with very affordable ammo costs.
Also, if she decides that she wants a bit more, I can move her into something like S&W SD9, a EAA Witness Poly, a Baby Eagle whatever so much easier than if she had taken her course with a revolver.