Publication order is perfectly valid. Here is some more context to help you figure out what to do. No matter what, your first stop is The Lightning Thief.

** denotes a companion book which can be skipped If you are just interested in Percy Jackson (Greek/Roman), then you could do the following: Percy Jackson & the Olympians

1. The Lightning Thief (2005)
2. The Sea of Monsters (2006)
3. The Titan’s Curse (2007)
4. The Battle of the Labyrinth (2008) **The Demigod Files (2009)
5. The Last Olympian (2009) **Percy Jackson & the Olympians: The Ultimate Guide (2010) The Heroes of Olympus
6. The Lost Hero (2010)
7. The Son of Neptune (2011)
8. The Mark of Athena (2012) **The Demigod Diaries (2012)
9. The House of Hades (2013)
10. The Blood of Olympus (2014) Percy Jackson’s Greek Gods (2014) and Percy Jackson’s Greek Heroes (2015) are myth compendiums that could be read anytime. There might be some minor spoilers for Heroes of Olympus. The Trials of Apollo
11. The Hidden Oracle (2016)
12. The Dark Prophecy (2017) **Camp Half-Blood Confidential (2017)
13. The Burning Maze (2018)
14. The Tyrant’s Tomb (2019) **Camp Jupiter Classified (2020)
15. The Tower of Nero (2020) Nico D’Angelo Adventures
16. The Sun and the Star (2023)
17. The Court of the Dead (2025) Percy Jackson Round 2 I believe these take place with some overlap to The Trials of Apollo.
18. The Chalice of the Gods (2023)
19. Wrath of the Triple Goddess (2024) Camp Half-Blood This series takes place during the events of Percy Jackson & the Olympians so you could read it earlier, but it is the most recent release (and more are to come)
20. The Wild Zone (2026) The two trilogies are in the same universe and can be read in sequence with publication but you could also skip if you are less interested. The Kane Chronicles (Egyptian)
21. The Red Pyramid (2010)
22. The Throne of Fire (2011)
23. The Serpent’s Shadow (2012) **The Kane Chronicles Survival Guide (2012) **Demigods & Magicians (2016) **Brooklyn House Magician’s Manual (2018)

Magnus Chase and the Gods of Asgard (Norse)

1. The Sword of Summer (2015) **Hotel Valhalla Guide to the Norse Worlds (2016)
2. The Hammer of Thor (2016)
3. The Ship of the Dead (2017) **9 from the Nine Worlds (2018)

edited for formatting.... fighting for my life with markdown