My 8 year old Daughter got the use of the family Marlin 101 (4 generations of shooters in the family have started with this rifle) Her 2 younger sisters have a few years before they get anywhere near them.
Next she gets the ar-7 explorer to introduce her to semi-automatics. Fun little rifle, Super light, able to Simply break it down and store in the stock,(maintenance lessons!), and the fact that it floats make it perfect for smaller hands and dropped guns in streams. I used to pick pinecones off the tops of trees... before my Dad taught me about trajectories.
The .38 is usually the next step once safety and maintenance learned. The family model 10 is a "bit" loose now after surviving for 70 years, and the cylinder gap is starting to let shrapnel out the sides. I think it's earned it's retirement.
I'll probably have to pick up a good .38/357 for her next step before letting her into the 9mm/.40/.45 colts.
I've yet to find a kid, who hated shooting a jug of water with a Hollowpoint.