The thing that always perplexes me about the "What gun should I buy for my woman" threads is that there seems to be an inherent assumption in the question that women are "special needs" when it comes to firearms. Unless she is a truly delicate flower of womanhood who will end up on a fainting couch if she hears a loud bang, chances are she has very similar requirements to a man's needs for a first gun. Something affordable, uncomplicated and reliable that fits her hands comfortably. Many would probably suggest a .38 revolver or a Glock for that situation.
The problem with asking this question is that it is similar to asking "What kind of car should I get for my lady" -- the solution space is too large to narrow it down without a lot of additional information. Many people would respond a lightly used Honda Civic, but then others will advocate a truck... Guns, like cars, are subject to personal choice considerations that someone on an internet forum just won't know about your loved one.
Spending a day at the range with her to determine what types of guns she likes and why could help narrow the field a lot. In fact, she probably won't even have to actually fire very many to exclude them from consideration (ergonomics, safety features not the style she prefers, etc.) Once she's narrowed it down to the few she doesn't dislike, then you can find some to shoot. If she doesn't even want to handle guns without firing them to find out which she prefers, she may not be sufficiently on board with this plan to get much benefit out of owning a firearm.
If it turns out that an HK P2000 or a Service Six is in that set of possibilities, PM me and we can probably figure out some way for her to shoot mine.