The main source is the Shahnameh, or Book of Kings (usually 'Persian Book of Kings' to distinguish it from the Biblical Book of Kings). It's essentially a chronicle of Persian rulers and the first section is heavily mythologized - demons etc, tales of heroes like Rustam. Penguin Classics released a decent translation a few years ago so it's a lot easier to find now than it used to be. It's also really interesting as it presents the Persian viewpoint of a lot of major historical events including but not limited to the wars with Greece and Alexander the Great (Iskander).
Another and more familiar option is the Arabian Nights. It's heavily coated in Islamic phrasing and imagery but the core of it is widely agreed to predate Islam, and it's a good mix of Arab and Persian stories. It's also very easy to read in short chunks; you can read a story before bed every night for a good long while and really digest it the way it was intended. Penguin Classics released it in three volumes (I, II, III).
There's another similar work called Tales of the Marvellous and News of the Strange which isn't quite as common or as well-preserved but has been released as a Penguin Classic (Bahamut Bless Penguin Classics) within the last few years so it's accessible as well. It's much more Arabic than Persian but there's a good amount of overlap and it's still something most people will be at least vaguely familiar with, without having all the details memorized. Makes for a good source.
Edit: Added Amazon links.