The investigation of the cases taken by Alice involve the other NEET Detective agency members and the leader of the Hirasaka gang along with the protagonist. As the series proceeds, more characters are introduced in the plot.
The series starts with Narumi being dragged into the Gardening club of his school by a classmate(Ayaka) and eventually into the NEET Detective agency as Alice's assistant.
Since the anime had something to do with a 'detective' agency, there was bound to be mystery involved in it. In the first few episodes, the viewers aren't provided with much information about the case, hence one cannot try to 'be the detective' in these episodes. However, with the plot involving a former member of the Hirasaka gang, the viewer is provided with enough information and I did spend a day trying to figure out what exactly must have happened(It turned out to be right after all :D). As the series enters into the last few episodes, it becomes a little boring and depressing. At least, I did not like the way it ended.
Regarding the characters, the protagonist seems to be the biggest 'weakling' among all and the person h matches closest to would be Ikari Shinji(from Shin Seiki Evangelion). However, later on, he does get a sense of leadership thanks to a small sacrifice.
As for Alice, she is a (super)hacker who is obsessed with Teddy bears and hates to go out. But one thing that I never understood was, how old is she anyway? That remains a mystery I guess.
The members of the NEET detective agency only seem to be useful for getting more information for Alice from what is not available in the database and rescuing Narumi when he gets into hot waters.
The leader of the Hirasaka gang, the Fourth and the former gang member Hirasaka Renji were probably the best characters in the series from my point of view because they were the ones who were independent for the greater part of the anime.
Overall, this anime got interesting after a few episodes but the excitement failed to keep rising and it got boring towards the end. That said, it was awesome for the greater part and did keep me excited about what would happen next. Once again, not as good as the other mystery genre animes I have seen, but definitely good enough to watch at least once.
