Jack and Jill went up the hill,
To fetch a pail of water;
Jack fell down
And broke his crown,
And Jill came tumbling after.
I can't think of a better way to explore rhythm and rhyme with a young child than sharing a collection of Mother Goose rhymes.
I have many favorite Mother Goose books. In fact, I have a shelf of them. THE TALL BOOK OF MOTHER GOOSE is the one I remember from my childhood. Rojankovsky's illustrations are full details that I loved looking for like Little Miss Muffet spilling her curds and whey. Though in truth, it looked like chicken soup to me.
There are many excellent Mother Goose collections available. The rhymes are an illustrator's dream, so look around and find your own favorite.
Another favorite of mine is the collection by Iona Opie, illustrated by Rosemary Wells: My Very First Mother Goose or Here Comes Mother Goose. FYI, the hardcovers are very big books. You will need a big lap for them. Some of the rhymes are available separately as board books.
Hey Diddle Diddle
The cat played the fiddle.
The cow jumped over the moon.
The little dog laughed to see such a sport.
And the dish ran away with the spoon.