Your child has decided that unicorns are the only acceptable subject, and will be taking no questions. What these seven have in common is a horn; what they do not have in common is anything else. Two are lap picture books for a three-year-old. Two are early chapter books your child reads alone. One is a comic collection for a fluent reader that you will end up reading yourself. Find the one that matches what your child can actually do right now, and hand them that one. Any single book here satisfies the whole path.
Sort this shelf by what your child can do, because the range is the whole point of it. Uni the Unicorn and Itty-Bitty Kitty-Corn are picture books for a lap, forty pages, ninety words. Thelma the Unicorn and Not Quite Narwhal are still picture books but they suit an older child, up to about seven, without embarrassing anyone. Unicorn Diaries and Unicorn Academy are early chapter books a child reads alone, and both are the first of long runs. Phoebe and Her Unicorn is a comic strip collection for a fluent reader of seven and up. Then pick your flavor. If your child wants the sparkly thing, Uni and Unicorn Academy are exactly and unashamedly that, and there is nothing wrong with wanting it. If they have started finding the pink ones babyish, that is a real moment and it has three answers here: Thelma, where a pony glues a carrot to her head and becomes a superstar and it ruins her life; Not Quite Narwhal, which is about a unicorn raised by narwhals and where he belongs; and Phoebe, which is dry and sarcastic and written half for you.