ORIGINAL: rem 700
Winchester 1300 if you can find one. Excellent guns. They cycle extremely smoothly, are perfectly shaped for the hands IMO, and work flawlessly. They aren't that high dollar either. Around the 870 range.
Thats another excellent choice in a slide action. Dang shame they quit making them. Still tons of great ones on the used market. If she is shorter in stature, the 1300 might be just the ticket. Winchester had the foresight to recess the pump slide's position when it battery, which makes it a heck of a lot easier for shorter arms to reach. One of the chief complaints with the youth model 870 is shooters cannot reach the pump to shuck the shells! Can be found on the used market for around $200.