Neon Genesis Evangelion and Great Teacher Onizuka. My two favourite animes of all time. And as a plus, they seem to fit your criteria nicely. They are both heavily based on character development and interactions, and both also have some action in it.
So ya, I heavily recommend those two, then if you want more, read the manga afterwards. They're both really satisfying because the GTO anime, although nearly 50 episodes long, only covers roughly half of the manga. And the Evangelion manga is written by Yoshiyuki Sadamoto, the character designer of the anime. So while it follows the same basic story, there are many changes littered throughout the manga. It's basically he's interpretation of the same story.
So in short, watch Evangelion and GTO, followed by their respective manga's. It'll be a very satisfying experiance.