The deal with reading Homer for pleasure, as opposed to class assignments, is to get a good translation. Academic translations of Homer can make the stuff terribly distasteful. Forget poetry or fidelity to Greek. Get one which has interesting writing in English. Grab a few, open them up, and check out the beginning of a few chapters. If you get flowery pseudopoetry, or verse, forget it. If you get something that reads like decent storytelling, grab it.

This is a war story: the Trojan horse, Achilles versus Hector, intervening Gods, Paris, the golden apple, etc. I prefer this to Odyssey.

Adventure story, lots of subtales of wacky adventures in wacky places dealing with wacky critters like Cyclops and his buddies. Most people prefer this to Iliad, below, but I didn't.