Preface: I ran into this question in real life -- getting kids I know hooked on Harry Potter. To my utter surprise, I realized we don't have this question on the site yet. So here it goes, in hopes that someone has an answer
What is the best reading order for the Harry Potter ancillary books? (Fantastic Beasts and Where to Find Them, Quidditch Through the Ages, and The Tales of Beedle the Bard).
Should they be read after all seven of the main books, or should they be read at different points during the main books? Or, for example, should individual sections of FBWFT be read in sync with which monsters are mentioned in the individual Potter books? Should The Tales of Beedle the Bard be read before or after Deathly Hallows?
Preference is given to answers based on J.K. Rowling's own opinion, but I am also open to well-reasoned suggestions based on pure logic, even if they contradict JKR.