Tons of good advice here already. Based on what you've said, let me offer one suggestion:
Let her find the one she really likes...and if it's past your budget, save up for it; it'll be worth it in the long run. If she's in immediate need for something for self-defense, it sounds as though you have a spare gun that she could borrow for a bit. If not, and you just need something to go bang, maybe pick up a Nagant and some ammo for <$100 as a stopgap.
If the gun which works best for her is $700 + holster and CCW, it's worth saving up for. Have the rest of your family chip in a few bucks when it's her birthday.