The Iliad (Caroline Alexander translation) is a much easier read and more entertaining than I expected. I had always heard it was the boring one compared to The Odyssey, and I'd read a lot of later Greek tragedies before but never any of the epics, so I had no idea what it might be like formally. I thought it might be more narrative with long lists of lineages that I'd have to trudge through. That stuff is in there to an extent, but a large proportion of it is people (and gods) proclaiming dramatic monologues at each other, which honestly makes it a real page turner as far as texts from thousands of years ago are concerned. (In retrospect, I guess it's not super surprising that something rooted in an oral tradition would be very monologue focused...)
A few belated additional thoughts on The Iliad:
(1) The amount of lineage stuff increased as the story went on, but it was almost all in the context of explaining how badass a central character is for killing someone who had has not been mentioned yet in the story. A lot of it goes like this:
But Achilles, his heart clad in valor, sprang for the Trojans,
shouting his terrifying cry. And first he killed Iphition,
the brave son of Otrynteus, leader of many men,
whom a nymph of the river bore to Otrynteus, sacker of cities,
below snowy Mount Tmolos, in the rich land of Hyde;
this man godlike Achilles smote with his spear across the middle of the head
as he charged straight at him; and the whole of the head was split in two,
and he fell with a thud. And over him godlike Achilles vaunted:
"Lie dead, son of Otrynteus, most terrifying of all men.
Your death is here, but your people are by Lake
Gygaia, where the land of your fathers is,
by the fish-breeding river Hyllos and the eddies of Hermos."
So he spoke vaunting, and darkness closed the others' eyes.
In other words, Achilles didn't kill just some nobody, he killed the son of a river nymph, who will now die far away from his homeland and with no proper burial.
(2) The story really does what it says in the opening lines! I thought it might give more resolution to the siege of Troy or Achilles' life, but it really is basically an account of a certain period of time when Achilles was really pissed off, and it ends when he is persuaded to stop being so pissed off.
(3) This is obvious, but seeing the gods' behavior really emphasized the degree to which modern gender norms get written onto them in modern popular culture depictions. For example, because Ares is a god of war, he frequently is presented in modern popular culture as tough and stoic, but in this he's a whiny little two-faced brat who runs to Zeus to complain when Athena fights back. (This isn't to say that there are not of lot of gender norms going on in The Iliad! One of the instigating incidents is a conflict over which warlord gets to keep a certain captured woman as his bride. That being said, certain gods often seem free to operate outside the gender norms for mortals, especially Athena.)
(4) A lot of the battles are more or less grounded in reality with gods basically casting buffs and debuffs, but there's a climax where Achilles quits moping to come back to the battle and the gods have a free for all that's really wild. One of the highlights is Achilles fighting a god that is a personified river. It's a great scene.
(5) I think people who want maximum accessibility might want to wait for the Wilson translation or try the existing Fagles translation, but having finished it now I do think that once you get used to its rhythms this translation is very readable, although there may be a bit of learning curve to adjust.