The Riordanverse in the order Rick Riordan published it, beginning with The Lightning Thief in 2005. Novels only - the crossover novellas are optional and not required to follow any of the main series. This order works well for new readers who want to experience the world as Riordan built it, with each series introducing new mythology while connecting back to what came before.
For readers who want to follow Percy Jackson's core story without the Egyptian and Norse mythology side series. Percy Jackson and the Olympians, Heroes of Olympus, and Trials of Apollo form a single continuous arc - these fifteen books tell one connected story from beginning to end. The Kane Chronicles and Magnus Chase are not included here but can be read at any point after the original Percy Jackson series.