I guess it would depend on how much money you would spend on a kids first gun. Mossberg makes the 100ATR in .243 "bantam" with a walnut stock that have a 12" L.O.P, or the "super bantam" that has a piece you can add to the synthetic stock at a later date to increase the L.O.P from 12-13". They are nice shooting guns that are inexpensive.
http://www.mossberg.com/images/Mossberg_Guns/930/NEW/26241.jpg

http://www.mossberg.com/images/Mossberg_Guns/930/NEW/26240.jpg