Children's First........

Children's Book for Entertainment :
  A collection of Rhymes called" A booke in Englyssh Metre", of the
Great Merchante Man called  Dives Pragmaticus.  It was printed in London in 1953.

First Story for Children :
The History of Little Goody Two-Shoes published by John Newbery in London in 1765, written by Oliver Goldsmith.

First Children Library:
 The Bingham Library for Youth in Salisburym Connecticut USA in 1803.

First Nursery Book : 
Tommy thumb's Pretty Song Book was published in London 1744. It contained wellknown  rhymes 'Hickory Dick dock and Sing a song of six pence'.