Discworld - preferably the City Watch novels. Books have been adapted a few times, but usually as lone events, and even the ones with a serious cast are just... okay.

Looking from one beloved dead author to another, Douglas Adams mercilessly chopped up the Hitchhiker's Guide between mediums. There was no "original version." It was all the same story, but sometimes with different events. That is the attitude necessary for capturing why Discworld is so good. Don't film a book, page-for-page. That's not how moving images work. Keep the characterization clear and fill in a storyboard from the Wikipedia description.

Anyway the real reason to go for a series would be consistent casting. Have the same guy play Vimes across a bunch of stories. Get cameos for Vetenari from the same wizened thespian. Call-forward future stories by turning bit-part scammers into Moist appearances, throw Gaspode in any scene with dogs, that sort of thing. Make Ankh-Morpork feel connected. Lived-in. Real, for a reality where wizards sometimes where fake glasses so people think they're badly disguised as wizards.