What kind of poems do children like?
Most children respond to poems that have a musical quality to them. That means lots of rhythm and rhyme.
Children tend to feel rhythm with their whole bodies. Watch a young child listening to music and you'll get what I mean. His whole body moves and sways and sometimes leaps. It's harder for him to sit still than it is for us "mature" types. A young child can be less afraid of looking foolish.
I've used the word "can" on purpose because unfortunately many children learn too quickly they'll be laughed at for looking "like a child." How sad for all of us when this happens. A child being a child makes something come alive even in grownups.
Playing with language and poems in particular is one way we can allow our children to remain children.
Poems are also helpful for children learning to read. Think about the rhymes of Dr. Seuss, for instance. Though not poetry per se, Dr. Seuss' books play with rhymes and nonsense and so teach phonics to young ones.
Poetry can do the same thing. A child who memorizes poems growing up has an advantage linguistically. Memorized poems also sit within the heart and can rise at moments when all other speech fails. Poems can help us think and feel more deeply than other kinds of writing.
For this reason having a treasury of good poems in the house can be priceless for a family. When that treasury is put together with children in mind, then the poems will be chosen based on their ease of entry. This doesn't mean they'll be trivial. A good poem is never trivial. But they will probably roll easily off the tongue and may include different types of poems -- both humorous and serious.