Jet Black is the best Bebop character. With "best" determined by how much responsibility a character has and the attention/development they receive.
He is relied upon as the
-Navigator
-Repairman
-Cook
-Captain (a patriarchal figure for the crew. Looks out for them all)
-Negotiator
-Finance manager
-and a bounty hunter
Everything falls apart if were not around, and you can't say the same for any other Bebop character. You get a glimpse of that after he leaves the ship to pursue a personal bounty in Black Dog Serenade.
He has two solo missions related to a past hang up - his missing arm, girlfriend leaving him unannounced, that end with Jet finding closure and moving on with his life. You learn a lot about Jet during these episodes. Not the case for Spike who remains an enigma until the end. He typically shares the spotlight during the Vicious arcs, and is never satisfied until he dies. If a theme of Bebop is confronting your past in order to progress in life, because you can never move forward if you're always looking backwards, then it's Jet who achieves that and not Spike.
Spike has the coolest design, the one Bebop character that you most want to identify with. But nobody really comes close to Jet in terms of importance, and only Faye can claim to match his characterization. I think he's the best example of what being an adult is like while Spike is more idealistic fantasy.
^ from Ganymede Elegy, one of his two solo missions. Probably the best character focused episode.