You're in for a wonderful ride. Discworld is among the best collections of books ever authored.
The (chronology written) first two novels were satirical romps. Once you get through to book three (Equal Rites) you'll start to see the core story structure that makes Discworld wonderful.
The flowchart of books is essentially showing what you could call the different series. It's mostly separating out the groups of characters that have ongoing themes book to book.
There's also some great analysis about Discworld and how the novels fall into three groups, mostly by when they were written. Terry Pratchett was learning about his world as he wrote it, his skills, and his desire to tell different stories changed over time. The net result are the early, middle, and late eras of Discworld.
The early age (satire & formation) goes up through about Moving Pictures. This was Pratchett staring to develop the world in general and being very entertaining along he way.
The middle age is a mature world building and his early exploration of deep topic, philosophy, and learning to tell bigger stories. That lasts up through about... (I'm looking at my wall poster to remember this stuff) The Fifth Elephant or The Last Hero-ish.
Then comes the lateer books and the payoff is world changing for the reader. Pratchett's world, storytelling, skills, and messaging have matured and it's a confluence like few authors ever reach.
You read Wee Free Men, which is in the third era and the start the Tiffany Aching novels. It's phenomenal! You'll see similar styles and very raw skill in the early books that led to Wee Free Men. You're in for a wild ride as you read Discworld, and I'm hoping you take some things away that really change your views of the world. Pratchett is just that good.
No, there's no best way to read Discworld. Just get started and you'll be well rewarded for doing so.