Why did Reese go to Hell?

Reese went to Hell because he felt he deserved it.

It's not an issue of Good or Bad but guilt.

As Lucifer explained to Reese...

L: I have a story for you, reporter. One I've never told a human soul before. I take no part in who goes to Hell.

R: Then who does?

L: You humans. [CHUCKLES] You send yourselves. Driven down by your own guilt. Forcing yourselves to relive your sins over and over.

And the best part the doors aren't locked.You could leave anytime. It says something that no one ever does, doesn't it?

R: No. You're to blame.

L: I am responsible for a lot of things, Reese, but not your soul, not your actions, and not whoever killed that poor girl downstairs.

Essentially, Reese felt guilty for trying to get Alvin to kill Lucifer, causing the accidental death and not being willing to accept that his marriage to Linda was over.

Just like @Paulie_D explained, it is a matter of feeling guilt.

However, it was a little bit more complicated in the original comic: it wasn't as much just a sense of guilt, but a sense that you need to be punished for your sins. If you felt that you should be punished for your "sins", you were punished, in a way more drastic than displayed in the show. This in a way, was turning hell into a heaven for masochists...

Just for a note: there were other ways to get to Hell: you could be sent there by a powerful entity (like a Dream of the Endless) or by selling your soul to any of the demons. Also, there were more than one hells - in the comic Lucifer goes to the Asian hell, where the sinners are being tortured with nightmares of the living.