gun shows are your friend!
Not quite, at least as much as they used to be. Most gun show dealers will try to fuck everyone out of their money unless you do your homework ahead of time.
Brand new Glocks can be had for less than your budget. Also, the CZ handguns are very well made and have a strong following. Most aren't polymer if that's not what you want, but they do have some plastic guns.
Most of it is really personal preference...If it were me and I had that kind of budget, I'd pick up either a new Glock or XD. Want to like the Glock better, but being a lefty the XD would probably work better. Would have no issue with a Sig either, great weapons.
Take her to a range that rents handguns, try and few and pick which one fits best for her.