It also depends on whether that 13-year-old character is already into manga or if this would be something new for him, too, because it would affect what your main character would recommend to his friend.

If the 13-year-old character is relatively new to manga, a good choice as the recommendation might be Fullmetal Alchemist. It's shounen, so it's geared towards teenaged boys, but it also has a lot of appeal for wider audiences, so your MC might think that the dad character might like it, too. At 27 volumes, it's fairly long for a newbie, but not really all that long for a shounen series. It's also famous and probably easily available, so it's a good choice in that way as well. Of course, that also means that if the 13-year-old is a dedicated manga fan, he's probably already read it.

It does have a fair bit of violence, since the setting is a military dictatorship and the events include the aftermath of a genocide among other things, so whether your characters would consider it appropriate for a 13-year-old would probably depend. If they didn't consider it appropriate, it could be the series that was rejected by the MC.