Here's a list of my eldest's favorite books THAT SHE COULD READ by the end of Kindergarten.
Note: she still needed help with some of the words, but she could recognize and read the majority of them. We read these books aloud.
Little Critter and the Level 1 series of Step Into Reading books seemed to be winners. When I'm looking for books for her to read, I try to keep them limited targeted at 1 to 2 shorter sentences on a page.
The Tooth Fairy's Night and A Green, Green Garden are at the harder end of her reading level. There's less repetition of the same words. Granted, she did enjoy Green, Green Garden because of the color words.
The collection of books above can be hard to come by. I HIGHLY recommend them. EG first came home with them from her teacher's library. We got our copies from a homeschooling friend with kids of similar ages. I was shocked she parted with them. They are funny and cute, high on the repetition side.
I hope this list helps you teach your little learner to read. Remember to keep a high volume of repeating words. The more practice they get recognizing the same words, the faster they'll memorize them and be ready to move on to new words.
10 Readable Books for Kindergarteners
A Green, Green Garden
Big and Little
Big Shark, Little Shark
Cat and Mouse
I Was So Mad
Tooth Fairy's Night
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As always, please check for these books at your local library, used-book sales, and other places that sell books. Some of these I purchased at Costco as part of box sets.