Epic poetry is a tradition of deliberate imitation: Virgil answers Homer, Milton answers both, and each expects you to hear the echoes. Reading in order, with a little mythological grounding first, turns that from allusion-spotting into genuine pleasure. The later poems literally cannot be fully read without the earlier ones in your ear.
The genre also runs dense with names and backstory, so a path that supplies the myths and a guide alongside the poems saves a lot of confusion. Here's a sequence that reads the epics as the conversation they are.
Ground yourself in myth
Start with The Greek myths, Graves's comprehensive retelling that gives you the gods, heroes, and family trees the epics assume. Pair it with The art of the Odyssey, Clarke's approachable study, so you know what to watch for. This groundwork makes the poems themselves far less daunting.
Homer and his commentators
Now the fountainhead. The Iliad is the wrath of Achilles and the tragedy of Troy; The Odyssey the long, wily journey home. Read alongside The Iliad: A Commentary (Vol. I), Kirk's detailed guide, which repays close attention to Homer's craft. These two poems set the terms for everything after.
Rome, England, and the tradition
Then the inheritors. Virgil, a study in civilized poetry by Brooks Otis prepares you for The Aeneid, Virgil's founding epic of Rome that consciously reworks Homer. Paradise Lost is Milton's vast Christian epic, answering the classical tradition on its own terms. Close with the critics who map the whole field: The Rise of the Epic by C. S. Lewis, The Western canon by Harold Bloom, and Epic and Empire by David Quint, which reads the genre against politics and power.
Follow the full path to hear each epic answering the ones before it.