For many years, I've worked with teachers and parents on how to choose children's books to fit their kids thinking beyond interest. Considerations are kind of book/media, type of literature, and finding a fit for the child's level of reading.
Libraries can be arranged in many ways and include so much more than just shelves of books. Scout out other book/media options such as magazines. There are many publications that reach out to children's interests and often have age ranges in mind with different variations created by the same publisher. Often the latest copy is in a ridged binder to help with wear and tear and on display. Often behind the display is a bin that has the last year's copies archived and you can check those out....go ahead and grab a handful! Audiobooks are another option. Libraries split their budget on computer files and disk/tape files. Listening to stories read by professional readers can help children learn to use intonation in their own head or voice while reading. Encourage your kids to do voices when they read out loud. In larger libraries you might find a collection of big books. These oversized copies are used by teachers to show strategies that good readers use. Your child can have their very own turn playing teacher and tracking from top to bottom and left to right, practice turning pages in the correct direction and catching details in the illustrations to help gain understanding of the written words. Board books are a wonderful way to put picture books into the youngest of "readers" hands to safely practice with a book before they learn book handling skills. The next time you visit a library, ask a clerk or librarian to show you how items are shelved so that you can navigate the many options.
A book is not just a book. We are familiar with with fiction versus non-fiction and generally have idea of how books are grouped in stores such as mysteries, how-to, and romance. For children, libraries usually group by different kinds of books. For the youngest readers board books and wordless books make a great start. Most picture books are written for preschoolers to about third grade. Easy readers or beginner books are written for children generally starting in kindergarten and grow with versions with chapters. Juvenile books are a broad category that cross all of your traditional school years with a heavy concentration in third through eighth grades. They are generally stories that children can related to and the length of the book is often not a one-sit read, but can be enjoyed over many days. Middle grade books are targeted toward upper elementary and focus on characters that are similar in age to those children. Young adult books have a broad range of ages from about 12 to 25. Once children grow into this area of the library, it is good to start with a talk about the various topics they may include. Author's sometimes write about situations with sexuality, abuse, drugs and alcohol or other circumstances that a character may be burdened with or trying to overcome. It is very helpful for children to be introduced to each section when they are ready to "shop" for that kind of book.
Libraries may also try to sort or identify books based on a local school system's reading programs. Ask the children's librarian if they collaborate in this manner. If your child does not know their level, find out either by contacting their teacher or having a running record done to identify the best fits for your child's ability. A great tool that has many picture books leveled is the Book Wizard by Scholastic. It is free to use. I recommend that parents or their kids use it to sort their own books at home by 1) too easy, 2) just right, or 3) not yet. Using their level, my recommendation is to allow children to choose books two levels down, on level or one level up for most of their reading time. Don't crush their desire to jump into a book by saying no to others. Those may good ones for them to read to a younger child out loud or to be read by a parent at bedtime along.
When it's time to grab a bag for books and go to the library, try to catch the children's or young adult librarian. Their schedules include many the branch hours or are they sometimes shared by other branches. Consider calling ahead to schedule an appointment. Sign up for reading incentive programs! Add a community program to your schedule such as a story time or art class that are offered in many branches. Also, feel free to jump from branch to branch as your card offers access to so much more then just the building near you. And, when you are ready to use your library card, remember to shop the library for types of books/media, different kinds of books, and that just-right fit for your child's reading level.