You don't indicate what sort of "target shooting" she wants to do. Smallbore Prone, Silhouettes, Plinking??? Then there is the question of a gun to fit her, (some gals are small enough to need a special gun). Also is this likely to be a long time investment or just something to get started with with the expectation of something else later.
All that aside, I Like to start new rifle shooters out with bolt guns and new shootgunners with break open guns because of the safety factor. I can easily see if they have the gun in a safe condition.