Suggestive readings for Persian (Classics and Oriental Studies at Oxford)Watch
Edit: I am currently reading Shahnameh, the **** Davis translation. I have read Khayyam, Rumi, Ghalib and Khusrow (just to say I am familiar with the style and themes in poetry).
For the latter you could probably just focus on reading about Persia in the Greco-Roman times, for example in Herodotus, and maybe also general historical background on the Achaemenid and Sassanian empires (also perhaps reading about Alexander and his phil-Persianism, if that is even a word!). For either/both aspects of Islamic religion in the region might be relevant, and for the Old Iranian option reading about Zoroastrianism would be relevant if you wanted to pursue Avestan. For both, although especially the Old Iranian option, some aspects of comparative/Indo-European linguistics might be interesting.
Not really a reading list as much as some random topics to consider, as I don't know any specific texts to suggest (other than Herodotus, Thucydides, Xenophon and Arrian all probably wrote on some aspects of Persia and Persians in their works at some point), but you can probably find primary sources in translation and secondary sources in English on most of the above if you pick a specific topic and look around the internet a bit (or see what kind of texts are used for similar modules at other universities).