There are dozens of origin stories. The Killing Joke (2014) goes the “one bad day” angle.

I personally prefer the Heath Ledger Joker as the best Joker.

He has no origin and he has no motive. He’s just a crazy MF’er that is intent on causing as much chaos as possible for his own amusement.

(Granted I did see a fan theory a few years ago that argued that there is evidence that he was an integral member of the League of Shadows, even possibly their lead explosives engineer. He either got tired of waiting for them to strike or got kicked out for being to crazy for them. I liked that theory too.)

As a comic book character Joker and his origin has many variations. The most common is that he was already a depressed low-level criminal (red hood). He gets chased by batman and falls into a chemical vat that results in the white appearance and green hair. The further societal exclusion makes him blame Batman and society which then becomes a feedback loop.

Joker has had strong implications with Harley Quinn (she was never solo in early work) and some others.

Killing Joke is more or less the approved origin story, although DC tries to be cagey about it.

As far as women goes, he was with Harley for a while, introduced in the animated show then made the jump to comics. Replaced with Punchline.

The Killing Joke is the closest thing to a canonical origin story, but like jordan said, DC doesn’t make it clear if that is official.

Personally, I like the idea of him not having a known backstory. It makes the Joker be to Batman what Batman is to most villains. The reader gets to know who Batman is, but to almost everyone in the DC universe, he’s an unknown person with unknown reasons for doing what he does. The Joker is that same thing for Batman.

The whole point of The Killing Joke is that Batman and Gordon prove that the ‘one bad day’ excuse is full of crap. People seem to miss that, including DC writers.