If you want the smoothest ride through the world Rick Riordan built, read the trilogy in publication order: start with 'The Red Pyramid', then go to 'The Throne of Fire', and finish with 'The Serpent's Shadow'. That’s the clearest progression of plot, character growth, and the slow reveal of Egyptian magic rules. I always feel like the pacing and stakes escalate perfectly when I follow that route.
After you finish the three main books, treat the crossover shorts as bonus scenes: the stories collected in 'Demigods & Magicians' (like 'The Son of Sobek' and 'The Staff of Serapis') are fun little crossovers that make more sense once you already know the Kane kids and Percy/Annabeth. You can read them after the trilogy, or slip them in later if you’re bingeing both myth series. Personally, I waited until after the trilogy and loved how the cameos landed—like finding extra notes tucked into a favorite book.