Since I started my journey as a children's illustrator, I've been approached by many authors who want me to illustrate books they intend to self-publish. And most of them think they need all rights to the illustrations - probably because there is so much misinformation out there.
Understandingly, most authors are unable (or unwilling) to pay a fair fee to an artist to illustrate a picture book ($5,000 and up for a typical 32-page book). On top of that, they expect to get all rights to the artwork for the less-than-fair fee. Traditional publishers that pay fair fees don't even do that. The industry standard to buy all rights is 100%-150% of the fair fee ($10,000 and up for a typical 32-page book).
Typically, the contract will give all BOOK rights to you, the author. Which means that the illustrator can't sell the art to anyone else to be used in another book, and you (the author) are free to use the art to promote the book. That's all you need!
Are you thinking: "What if my book gets so popular that I want to license my characters to make plush animals or action figures out of them to sell?"
I'm really glad you have so much confidence in your book - that will take you far! But, in reality, this probably won't happen, and if that highly unlikely scenario does play out, there can always be re-negotiation talks for more rights.
I think it's sad that so many first-time authors won't hire an artist who won't give them full rights. Most professional illustrators won't agree to do that, so the talent pool for the authors to choose from is shrunk to the inexperienced and unschooled in the industry. I feel like a lot of authors are really shortchanging themselves from having great art for their stories because of this mostly irrelevant issue.
If you are thinking about self-publishing, and put all the time and effort into writing and marketing your story, please consider how important the visuals are! The better the art, the bigger chance for your book to get read! And who is going to want to buy a plush of a mediocre character anyway?
Something to think about.