Berenstain, Stan and Jan "The Berenstain Bears" - 1962ff.
My kids loved the Berenstain Bears. Not only was it a "normal" family, the characters just happened to be bears, but it was a funny family. They live in a lovely tree house, and there are hundred different books with all kinds of subjects, anything that can happen in a child's life must have their own book, from the arrival of a new baby in the family to moving and going to the doctor, from starting school to all sorts of holidays and activities. A wonderful set of stories for children, often written in rhyme form but quite easy so that early beginners can enjoy these books just as much as little children who don't read, yet.
Some of the books we enjoyed enjoyed:
The Bear Detectives
The Bear Scouts
The Bears Picnic
The Berenstain Bears Forget Their Manners
The Berenstain Bears Go to School
The Berenstain Bears Moving Day
The Berenstain Bears New Baby
The Berenstain Bears and the Prize Pumpkin
Get in a Fight
He Bear, She Bear
The Messy Room
The Berenstain Bears' New Neighbours
No Girls Allowed
Old Hat, New Hat
The Berenstain Bears and Too Much TV
Trick or Treat
From the back cover:
"THE BERENSTAIN BEARS' First Time Books® are all about new experiences children encounter in their early years. With good-natured wisdom, love, and gentle humor, these books ease the way for kids - and their parents - through these first times"