Shahnameh is certainly the greatest monument of poetry in the real Persian language but by considering a large number of Arabic words which are still used in the modern Persian language, Divan of Hafiz can be said to be the only Persian book which can be found in almost all Iranian houses and everyone enjoys reading it.
However if you ask an Iranian to recite from memory a Persian poem, in all probability this poem will be from Bustan of S'adi, because from the childhood we have learnt to read his poems in the schools and other places, but there can't be more musical poems than Rumi's poems, you can read them and dance.
Rubaiyat of Khayyam seems to be the most translated book from Persian and probably that is the most known Persian monument of poetry, Khamsa of Nizami consists of the most famous stories in Persian literature, especially its legendary love stories, it can be said these are the best Persian musical movies.
There are also several other ones, which one do you think is the greatest?