The main series is super straightforward: start with 'The Lightning Thief', then 'The Sea of Monsters', 'The Titan's Curse', 'The Battle of the Labyrinth', and finally 'The Last Olympian'. That's your core story right there. Most folks you ask will tell you to stick to that order first time through.
But honestly, the fun part is how Rick Riordan built everything out. After you finish, you can dive into the sequel series, 'The Heroes of Olympus', which starts with 'The Lost Hero'. That one continues the storyline with some new and old faces. There's also 'The Trials of Apollo' that comes after, though some fans feel the tone shifts a bit.
Just a quick warning—avoid the movie versions if you're looking for accuracy to the books, they're... quite different.