We purchased a "starter" rifle for the Granddaughter this fall, a Ruger American Compact in .243. The rifle proved to be decently built and is surprisingly accurate for an entry level rifle. If ammo had been more available, I might have gone with a 7/08 and reduced recoil ammo (she is 9 yrs old). She did fine with deer loads in the .243 and it worked well for her size with it's compact design.
The plan is to have this rifle be the beginning rifle for all the Grands and as they get older, something more versatile will be acquired.