To self publish a children's book is expensive. It does depend on a lot of things. Your illustrator. How much color you use. If you look for a good priced printer. Get Idiot's Guide to Self Publishing. There is a lot of info in there.
If you sold it to a publisher you lose a lot of your freedom. They choose the illustrator. They can change your title. They decide the shelf life. They pretty much do everything. It is a load off of your shoulders but if you want your book the way YOU want it you should self publish. Of course there are probably special circumstances. I am a beginner myself and am trying to collect info.