This sounds so fun. So many ways you can go there’s no right answer. Just to throw some thoughts out there you’d first want to consider the target age group so that it’s written with the child’s comprehension and interest in mind.
As for art, unless you have art skills, there are so many great artists that are fans out there. See one who does work you like in the right style? Ask them to illustrate your book as a fun project.
Now if it was me, (I’m a writer myself) I think it would be cute to do a series, a book for each era, but with cartoon images of Green Day as little kids, but in their iconic looks for each one (Dookie, Nimrod/Warning, AI, etc), each book telling a simple story around being in a band and making music, focusing on friendship and doing what you love.
What do you think?