The first book matters less than the second. A series lets a new reader keep the characters and spend their energy on the words. Biscuit, Fly Guy, Pete the Cat, Elephant and Piggie, and Henry and Mudge all work this way. So does Dr. Seuss, if you count the shelf as a series.
Hand them book one and stay in the room. When they finish, show them that another book about the same dog, fly, or pig is waiting. Do not make them earn it with a harder title.
Green Eggs and Ham belongs here because children will reread it until the words are theirs. We Are in a Book! belongs here because they will explain the joke to anyone who walks in, and explaining is reading.
If a series clicks, stay with it for a month. Jumping to a new kind of book every week feels like starting over.
Keep book two where they can see the cover. The series works because the next face is familiar. Hide the pile and you hide the reason they wanted to finish.