Lots of options ...
I would suggest a lesson from a local instructor / let them supply the guns - see if you can settle on a gun that fits her. A lot of ranges have rental guns / or guys may let you borrow a gun - to help you out.
Don't buy her a gun until she's ready to understand what she likes /what really fits her.
For new shooters I use a couple of different guns / especially for ladies ( including my granddaughters, etc ):
1. A semi-auto 20ga / something light ( around 6 1/2 lbs ) so they're strong enough to swing the gun. My preference is the Benelli Super Sport at around $ 1,800 / but there are a lot of gas guns - Beretta, Remington, etc for around $ 1,000 that are good options too.
2. I use a 28ga O/U / mine are Browning Citori XS Skeet models - retailing around $ 3K. But 28ga guns / and especially shells are very expensive unless you get into reloading. A 28ga is probably not a smart budget option - and inexpensive O/U's are prone to all kinds of problems in all gagues. But if a friend has a 28ga you can borrow - its a good option for a new shooter.
3. A 20ga O/U - and there are lots of them around used / but don't buy a gun until she's ready to know what she likes. / or maybe a 20ga pump gun - like a Browning BPS Hunter model is a pretty good option.
4. If she has more upper body strength - maybe consider a 12ga / but keep the loads light, so recoil doesn't ruin it for her. 7/8 oz loads at 1150 fps is a smart choice on 12ga ammo for a new shooter in a 12ga.
Make the outing fun / when she's had enough / shut it down. Shoot station 7 on Skeet / or lock a Trap into one position .... help her understand the gun mount, see the target, don't look at the barrel, feel the lead ... the concept of shooting a "shot column pattern" like a handful of gravel you would throw at something vs a "bullet" going downrange ... lots of good DVD's out there too.
But start with a lesson / some loaner guns .....go slow...