There's plenty of kid-appropriate manga and anime available, the question would be best answered depending on the boy's interests. For example, my nephew, who's about the same age, would love a good sci-fi manga (can't think of any titles offhand, unfortunately) because of his love of astrology and science.
My recommendation would be to look on amazon.com first by type (genre) and then by age group. They're pretty good at sorting such things.
Another good place to look would be manga publisher sites such as Darkhorse or Tokyopop, since they do sort by genre and age usually. Then you have to take into account that something appropriate for a Japanese 10-year-old is usually translated for an older audience here in the states.
Unfortunately, there really isn't a solid answer anyone else can offer to this question, since as I said it depends on the boy's interests. If he likes board games, a good one might be "Hikaru no Go." I haven't gone looking to see if that one's made it as an anime, but it's an interesting manga that includes a little Japanese history, since "Go" a chess-like game traditional in Japan.
Anime is something that could easily be figured out through, again, publishers. Viz entertainment did a number of anime frequently for kids. The same for Pioneer and Dic. It's a matter of you doing the research based on his interests.