Both of my girls learned to shoot with an NEF break-action single shot .22. Easy to focus on fundamentals of sight picture and trigger press. Also easy to keep track of hammer position. One daughter stayed interested in rifles and now has her own Marlin 795.
I bought the youth combo that also has a .410 barrel. Just recently, my young rifle girl expressed interest when I hit the dove fields, and we swapped barrels so she could learn shotgun fundamentals. Though it is not an ideal shotgun, it is light and compact, and made it easy for her to gains some success fairly quickly.