There is a very wide range of children's book art styles. From realistic to cartoony and everything in between. All the classics I can think of have nothing whatever in common with one another--stylistically Maurice Sendak's Where the Wild Things Are looks nothing like a Dr. Seuss book or Eric Carle's The Very Hungry Caterpillar. Heck, Sendak's work is even dark, and you'd expect that would be a no-no for children's book illustration. Just be true to yourself and your interests as an artist. Maybe think of your audience as your younger self, and ask what you would have liked when you were a child when you decide where you want to go with your art and stories.
If you are working in a self publish situation then you may get some notes and art direction from the author since in those situations they tend to be the ones paying for the art. For most publishers, the ones you see at book stores, the author has very little say in who the illustrator is. Only very famous authors have some say and even then largely its a suggestion and not a demand. The art director for the publisher chooses the illustrator and that is who the illustrator answers to, not the author. It's not uncommon for an author and illustrator to never even speak or meet during the books creation. This is done largely so that the artist can create their vision of the book. They read the script and they visualize what the story will look like to them and execute it. The illustrator is hired for their style and imagination. Forcing them to try and make the drawings match what the author envisions hampers that.
To your original question. There are no hard rules for how you draw what you draw. It just needs to make sense to your style. However, there are a number of general requirements for the types of artwork and subject matter an art director would want to see in your portfolio to be considered for a job in the trade children's boom market.
For a publisher a competent writer/illustrator is a great thing! It's also fairly rare. Most great artists aren't great writers and most great writers aren't great artists. So it's rare to find a person who works at a professional level in both areas. Even then writing a story doesn't always mean that you would be the best artist for it. Different stories call for different artists or aesthetics the way that different movie scripts call for different directors.
It wouldn't necessarily save money. If you write and draw the book then you should get paid what a writer would get paid as well as what the artist would. (Which would be a GREAT check!!) The only way it saves you money is if you are self publishing then you don't have to worry about coming up with the funds to pay an artist. You may still need to solicit the skills of a designer. Your book would still need to be layed out, typeset and made ready for publication.
Look -- the publishers buy the kind of art they think will cause the public to buy their books. That is the only rule. If you want to do some research, go into a bookstore or library and look at children's books. That is the kind of art publishers are buying.