Originally Posted by trebark
All the of the calibers you list will do the job as you describe it. So pick which one you like and go with it. I would say the key to your barrel would be to get a fast enough twist so that she can shoot the heavier 6mm bullets at longrange when she's ready.
The tougher part of the project will be to have a stock that can grow with her.
Also, important to girls is noise. Most girls do not like a lot of noise. So be sure to get her a good pair of earmuffs.
Actually the stock is easy. Go with a full sized adult wood/laminate stock, cut it to fit LOP and keep the cut off block.
Before it's cut you have the smith drill dowell holes past the point of cut off.
Then when the girl/kid grows to where it's time for the full lop, you replace the cut off piece using dowels, sand and refinish and you'll have a perfect match.