Spirit Detective Is a Job, Not a Chosen-One Title
Once Yusuke is alive again, Koenma recruits him because his near-death experience has made him unusually sensitive to supernatural activity. The title sounds grander than the early work actually is. Yusuke gets assignments, tools, partial explanations and exactly as much support as Spirit World bureaucracy thinks he needs.
The stolen Artifacts of Darkness case establishes the pattern. Gouki, Kurama and Hiei are all demons, but the case immediately teaches Yusuke that "demon" is not a useful moral category by itself. Gouki preys on children. Kurama is trying to save his human mother. Hiei is dangerous and selfish, but later becomes an ally.
Why it matters
Yusuke's best quality as Spirit Detective is that he never becomes very good at treating Spirit World's categories as unquestionable truth.
Debut: Ep 006 - Three Monsters
Kurama Chooses His Human Mother
Kurama steals the Forlorn Hope because his human mother is dying. The fox demon who originally entered a human body as a temporary refuge has lived as Shuichi Minamino long enough for the relationship to become real.
That is the detail to remember whenever later arcs bring Yoko Kurama back. Kurama is not a demon pretending to care about humans. By the time Yusuke meets him, the human life he expected to discard has already changed what he values. He is willing to trade his own life for his mother's before Yusuke intervenes.
Why it matters
Kurama's entire series-long identity conflict is already present here. The question is never whether Yoko or Shuichi is the "real" one. Both are real, and Kurama has to decide what kind of person those histories make together.
Debut: Ep 007 - Gouki and Kurama