Your child wants manga. Maybe a friend has it, maybe they've watched the show, maybe they just like how it looks. And you've picked one up in a shop, opened it from what you thought was the front, found a page you weren't expecting, and quietly put it back. That's a fair reaction. Manga isn't one thing — it's a whole publishing industry, and plenty of it is written for teenagers and adults. But a real chunk of it is made for children, and it is fantastic for a child who won't read. This shelf is that chunk. Any single one gives your child the whole experience, so pick by their age and what they already love. I've been specific about which ones read backwards and which one isn't for a younger child at all.
Two questions decide everything on this shelf, so I answered both for every book. First: what's actually in it? Manga volumes run long and the content shifts between them, so I went to the publisher's own rating rather than trusting the cute cover — VIZ and Yen Press both rate their books, and where they say 'All Ages' I've checked what that covers, and where they say 'Teen' I've believed them. Second: does it read backwards? Most manga is printed in the original Japanese order, so you open it at what feels like the back and read each page right to left, top-right panel first. Every book here except one does that. It sounds like a barrier and it isn't — children pick it up in about ten minutes, faster than you will, and most volumes print a little 'stop, go to the other end' page to help. Chi's Sweet Home is the exception: it's full color and reads left to right like an English book, which is why it's the easiest door on the shelf. Because this is a shelf, nothing builds on anything. Reach for the one that matches your child's age and their obsession — the cat one, the funny one, the Zelda one, the game ones — and skip the rest with a clear conscience.