By J.K. Rowling
Harry Potter's core story is told across seven novels, beginning with Harry Potter and the Philosopher's Stone and ending with Harry Potter and the Deathly Hallows. Publication order is also the story order and is the clearest route for every first-time reader. Harry Potter and the Cursed Child is a later stage-play script: read it only after Deathly Hallows, and treat it as an optional continuation rather than an eighth core novel.
Start with Harry Potter and the Philosopher's Stone and read the seven novels in publication order. Cursed Child comes afterwards but is an optional stage-play script, not an eighth core novel.
The 8-part film series closely follows the 7 core books (with the final book split into two films). If you've seen the films, you can confidently start with the first book, as the novels contain a wealth of detail and subplots not shown on screen.
Publication Order: The Harry Potter series should almost always be read in publication order. Each book represents one year at Hogwarts, and the overarching plot involving Voldemort builds sequentially from book 1 to book 7.
Chronological Order: In this case, publication order and chronological order are identical.
2000