Another option would be to buy a youth .308 and start her out with Managed Recoil loads. Managed Recoil loads typically cut recoil by 50% and for a .308 that would probably put it around 8ft-lbs of recoil which is about what a .243 will deliver. When she gets older and bigger she could easily move up to hotter cartridges. If she grows up petite she may never out grow the rifle and she would have a rifle that is good for all big game in the lower 48 assuming she can handle a standard .308 load. 7mm-08 is a great option as well as it delivers about 12ft-lbs of recoil force. Not sure if remington makes managed recoil loads for 7mm-08 or not.
Here is a picture of my niece with her Savage Edge Youth Rifle in 7mm-08 Caliber. She took her fist buck this past year in the San Bernardino Mtns (Unit D-14) located in southern California. My niece is 12 years, she is small frame and weighs about 80 lbs. She loves her new rifle.
Thanks for all these ideas on the thread. My wife, is very petite. She was in the Army and Navy in her youth but ended up getting a medical discharge in her service in the Army shooting a rifle that threw out her shoulder. She has expressed wanting to shoot with me and try it again, perhaps hunt too. Some of these options mentioned with managed recoil loads, etc seem like it would be a good fit for her without just having her limited to plinking with the .22. Her shoulder has long since healed but I've been leery on her trying something more than a .22 that might cause her to get hurt again.
Just wanted to say thanks to everyone as this youth thread is giving me some ideas/options also for my wife.
A ruger hawkeye in 257 Robert's would be a great rifle for a kid, especially if you hand load for it.
Look into TC Encore many calibers and weight not to bad