You need to do some research. Children's writing is a very specific genre. You could look through the 2005 edition of "Writer's Market" and see who is looking for children's books. If you want to try for a large publisher you will need an agent. For that, library reference desks have a directory of literary agents. Each agent and agency lists their specialties, and you can see who is interested in representing children's books. To learn how to write a proposal, "The Shortest Distance Between You and a Published Book" by Susan Page (Broadway Books) is an excellent guide. There are also guides to proposal-writing on he web.

Self-publishing works best when you have a built-in way to sell your books, such as classes that you teach or concerts that you give where you could sell them. Bookstores generally don't carry self-published books. Some people are very successful with self-publishing, and others end up with a garage-full of books that they can't even give away to their friends. So you want to think things through carefully before taking that route.

Good luck.