As others have... kind of.. said..
You only need the Atlantean Edition Conan RPG in order to play the game. No other books are necessary.
You can access to the d20 SRD if you need to access the core d20 rules for some reason. But if you can -- it's never a bad idea to have the core D&D books (Player's Handbook, Dungeon Master's Guide, Monster Manual) around. But again, they're not necessary.
Likewise, the various Conan supplements, such as Hyboria's Fallen, Scrolls of Skelolos, and The Road of Kings, as other posters mentioned, are excellent additions to your game but -are not NECESSARY-.
Short Answer: You only need the Atlantean Edition Conan RPG core book. Enjoy.