SIG
9mm or .45 if she can handle it. Personally, I can't shoot my .40 S&Ws all day because it starts to dig into my skin and I don't want to wear shooting gloves. Also, the velocity may not be the best for home defense. For home defense, I would prefer .45 simply for the slower velocity and it stopping. 9mm, you can shoot all day, but it may not stop and go through multiple walls. IMO, if she can't handle the .45, I recommend 9mm.
Also, Glock is very reliable, but I don't like that it doesn't have a safety lock. It is basically a mechanism built into the trigger which I hate, that and its plastic. But I know many people who love them. Note, a women that I went shooting with couldn't shoot her Glock because she sort of limp wrists it, so the natural recoil kept jamming the ammo. But I shot it and it was fine. I replaced the trigger to a 3.5 pound trigger pull and it still kept jamming on her. Glocks are great guns though despite my aversion.
If it was my money, SIG all day every day, but I am a SIG guy. IMO, go with her to the store and have her actually grip the guns and pick the one that is most comfortable. Some women don't like the double stacked mags and some do. The same woman who couldn't shoot the Glock loves shooting the single stacked 1911 .45 so go figure.
Hope this helps, and practice practice practice. Remember, the ammo nowadays is more than the guns itself. Take that into consideration too.