Another great, relatively easy manga I've been reading lately is Detective Conan (名探偵コーナン). It has furigana over all the kanji, and the subject matter is pretty normal, so I find that I can usually infer the meaning of words I don't understand (I read it without a dictionary).
Note that many Japanese children's books, particularly picture books, tend to be written almost entirely in kana, which can make them quite difficult to read (as opposed to kanji with furigana).
Edit: while we're talking about getting books, let me add that for the lucky few that have one in their area,
BookOff is by far the best place to buy manga. Used manga there sell for 105円 (less than a dollar) in Japan. I've been to the New York store; I don't remember how much they charged there, but it was really cheap. Londoners, if you have a friend in Paris or near a US or Japan store, it may be worth it to get them to buy some for you and ship it!