I'd suggest a .22 revolver--a K-frame Smith & Wesson, or a Ruger single-action. Ammo is cheap, the gun will be easy to shoot (espeically if you can find a Smith with a good trigger), and she'll get good with it pretty quickly. When she's very comfortable with the .22, move her up to a .38 Smith target revolver.
The revolvers are easy to clean, too.
thanks for the 411. She is really excited about getting started.