Some just use the books in the centers, while others allow the children to take the books in the centers, while others allow the children to take the books home for the family members to read. This often resolves the problem of parents getting to the library with their children. Decide how you will evaluate the effectiveness of the project. See the funding opportunity page for grant ideas. Make plans for how you will sustain the project and plan on replacing items as they get worn.
Some libraries just pick four to six good children's books and videos for different age groups.
Child care providers may prefer themed kits, while parents may prefer the convenience of grabbing a preselected set of materials they can read with their child. If you're just starting out, you may want to start simple with books and a puppet, for example, depending on your objectives. Many libraries include games and manipultives which require more staff time to count and account for, but they are popular too. See the resource section for great ideas from other libraries. Use stickers or stamps to identify the books that belong with the kits.