We have a Savage Cub with a 4x rimfire scope on it which works well. My girls are 10 and 13 now and it still is a good fit. We have had it since the 13 year old was 6 or 7. They shoot it near rapid fire now with me holding a box of bullets off to the side.
The Savage Cub is a pretty good gun. It's trigger is a bit heavy and rough, but they can learn it well enough.
A red dot or low power scope is key to fun. Also, shooting at 5 - 15 yards is a good place to start. Aluminum cans are a fun first target after you sight it in.