The Discworld Series is expansive. Most fans of the series do not recommend starting with the first novel and reading them in chronological order by date of publication. One way to get started in Discworld is to choose a protagonist and follow their story. Along the way you meet other great characters who might also interest you. Maybe some characters will not interest you, and that's OK too. The characters are presented here in no particular order.
Tiffany Aching is a young witch we first meet in the Wee Free Men. When we encounter Tiffany she is 9 years old and even though she is not yet a proper witch she finds herself both doing battle with and befriending magical folk. Throughout her story the Nac Mac Feegle continue their friendship with her. The Nac Mac Feegle are a rowdy bunch of celtic-esque fairy folk more akin to mischievous pixies than fairies as they often depicted in current mainstream fairy tales.
Esmerelda "Esme" Weatherwax is also known as Granny Weatherwax or Mistress Weatherwax and is arguably the most powerful witch on the Disc and appears in 7 of the Discworld novels. She is ornery, opinionated, and a practitioner headology. Granny Weatherwax prefers practical, hard work to the use of magic for most tasks but is a magical force to be reckoned with should the need arise.
Death is, of course, a grim reaper character who appears in almost every Discworld novel. Unless he insists that someone sees him, Death is only recognized by those with magical inclination such as wizards, witches, and children, and cats. Death is very fond of cats, and curry. Unlike other personifications of death, Discworld's Death is a likable guy who is both fascinated and bewildered by humans.
Moist von Lipwig is a con man who turned civil servant after surviving a hanging. Moist von Lipwig has a bit of mysterious past that includes several aliases and an easily forgettable appearance.
Rincewind is the first Discworld protagonist appearing in The Colour of Magic, the book that started the series. Rincewind is the quintessential un-hero. He failed as a student of wizardy at Unseen University and has an equaled knack for turning the smallest difficulties into massive problems. Rincewind would prefer to live a boring uneventful life but finds himself adventuring despite his best efforts to avoid it.
Samuel "Sam" Vimes is the ne'er-do-well who becomes part of the social elite. No physical description of him appears in any of the Discworld novels leaving fans to develop their own image of the drunken copper who becomes Commander of the City Watch, a knight, and a duke, whether he wants to or not. Sam Vimes is both an idealist and a cynic.