I love that you are reading with your son! My parents read to us all the time growing up, everything from novels to collections of short stories, and those time remain some of my best memories. Here a short list of some things I remember reading when I was that small:
The Tales of Peter Rabbit by Beatrix Potter
The Velveteen Rabbit By Margery Williams Bianco
The Chronicles of Narnia series by C.S. Lewis
The Children's Book of Virtues by William J. Bennett (A collection of short stories)
Matilda by Roald Dahl
Jungle Book by Rudyard Kipling
Little Pilgrim's Progress by Helen Taylor
White Fang - Jack London
I also remember loving James Herriot stories. He was a vet and writes short stories about animals. Some of them are more mature, but he also has collections more geared towards children.
My parents read us books that were probably well above our age level, but they would reword things so we would understand. They also read from abridged versions of classics because they wanted to love good literature and felt a lot of more modern children's books were vacuous.