I usually raccommend this book. It has some kanji (not many) and furigana on them. It is written in bi-language even tho the English version could be a guideline, but far from a literal translation (in fact a few times I had to ask for help in this forum). The book is at kids' level, I mean phrases construct is kept rather easy and not with multiple relative clauses or weird verb constructions.
Remember tho that it is a book written for kids and not always they are the easiest to read, plus stories are mostly about old people so I guess the way of talking is a little bit different...that is what I was told when I asked to explain me the construction of a phrase whose meaning I could understand, but not the construction. The phrase is the following よめをとらんといかんのう...I wrote so that you can have an idea of what certain phrases might look like. In this phrase for example the author didn't use any kanji (which are 嫁、取る、行く), while in other cases he uses kanji in the whole phrase.
Up to you...btw, stories are kinda simple with a plain moral...just the ones you tell kids.
Sasuga Books
EDIT: Glad I always check the links I give. Don't know why, but it won't give the page of the book directly. However from that link look at the top left side of the page. In the quick search there is already the title in...just click GO.