For the mythic logic, read The Iliad first, then The Odyssey.
The Iliad places Troy, Achilles, Hector, Agamemnon and the Greek war.
The Odyssey comes after: Odysseus has survived Troy and seeks Ithaca.
But to prepare for Nolan's film, The Odyssey alone is enough.
The horse, the fall of the city and several returns belong to the wider Trojan memory.
Option 1: Iliad then Odyssey
This order lets you feel the passage from war to return. The Iliad shows heroic honor under pressure; The Odyssey asks what happens to a hero when war is over but peace has not arrived.
Option 2: Odyssey first
If the film is your horizon, start with The Odyssey. The poem gives enough to follow Odysseus: his absence, his desire for Ithaca, Poseidon's anger, the episodes at sea and the occupied house. You will lose some Trojan depth, but not the heart of the announced film.
The limit to remember
The Iliad does not narrate Helen's abduction in detail, nor the whole war, nor the horse, nor the complete fall of Troy. It is not the modern "novel of Troy." It is a poem concentrated on Achilles' anger and its consequences.
Practical paths
Questions of reading
Should I read The Iliad before The Odyssey?
It is the most logical order if you want Troy first and the return second, but it is not required.
Can I read The Odyssey alone before Nolan's film?
Yes. For The Odyssey, the poem itself is enough if you know the broad context of Troy.
Does The Iliad tell the whole Trojan War?
No. It focuses on Achilles' anger and ends before the horse and the fall of Troy.
Which edition should I choose?
Choose a readable translation with notes, then return to the key passages if you need a shorter route.