I had a book published. It was a lifelong ambition but I didn't make any money out of it. Don't send your manuscript to a publisher. They have neither the time, inclination nor the staff to indulge unsolicited submissions from new authors. You need to work through an agent as publishers work through them on the basis that the agents filter out all the dross and proceed according to their recommendations. However, agents will not hesitate to bin you off and most do.
There used to be (and may well still be) a writer's annual handbook with many agents' details and various tips about submissions. The first thing to do is check out those specialising in (or at least working with) children's books and concentrate on those. You'd need to verify that they accept unsolicted submissions and exactly what they require.