Once you have narrowed your options down to a few editors, five or less for example, set up some initial contact with each of the children’s book editors. Start by contacting them and see if they can answer your core questions via email. Find out if they are willing to chat with you by phone or skype about your project when you are ready to make a decision. Ask for them to specifically identify what children’s book editorial services they will be able to provide.
It’s always sensible to follow due diligence in submitting your first draft of your book to an editor by making as fool-proof a copy as possible for you because first, it is your own creation, and secondly, a horrid draft sent your editor can end up frustrating both you and him or her. Make your own corrections to the extent you can, so that will make the job of your editor that much lighter and the end result would be a lot more effective.