I don't think a huge amount of context is needed really: the main bits of knowledge that the Iliad takes for granted are

• there's a war going on;
• the Trojans and their allies are based in the city, the Greeks have a camp by the sea;
• some of the main characters.

The last item is the one that causes the most problems, because the names do pile up in places, and it can be disorienting if you don't know which ones to pay attention to. The opening book has several characters that seem like they're going to be regulars, but they turn out to be bit parts. That kind of thing. So an edition with a glossary of names at the back would be a good call.

Just briefly, the characters you need to pay attention to are --

• Greeks: Achilles, Patroclus, Agamemnon, Menelaus, Diomedes, Nestor, Odysseus, Aias

• In Troy: Hector, Paris/Alexandros, Helen, Priam, Sarpedon, Aeneas

• Neutral-ish gods: Zeus, Thetis
  Gods allied to Troy: Apollo, Aphrodite, Ares
  Gods allied to the Greeks: Athena, Hera, Poseidon

If you can digest this, you may not even need a glossary of names.

Most modern editions are fine. Caroline Alexander's translation is a notable one from the last ten years, and she's got a poetic style, but it sounds rather biblical and the notes aren't as extensive as some others. Stanley Lombardo's translation has the best track record among new readers. Also popular are the ones by Robert Fagles and Robert Fitzgerald. I have a personal fondness for Rodney Merrill's. All of these would be fine.

I do however have some recommendations on ones that you should avoid.

• Richmond Lattimore. His version is excellent, and it's been a standby in college courses for generations. Lattimore does have a fine literary quality. The problem is just that it's too damn hard. It feels contorted.

• Stephen Mitchell. His version leaves out most of the epithets (the things that actually give Homer his flavour), and he leaves out book 10. Regardless of the reasoning, book 10 is part of the Iliad as the ancient Greeks knew it: it's irresponsible to pretend it doesn't exist.

• Old translations. They're not necessary bad or wrong -- well, not all of them -- it's just that I'd recommend a 21st century reader go with a version designed for a modern audience. This includes: A. T. Murray, Samuel Butler, Alexander Pope, E. V. Rieu, and many more. Note that Rieu's version is still available in a Penguin edition, and it's almost completely flavourless. Murray and Butler are widely reprinted and available online, because they're out of copyright, and I think they're both awful.

Overall I'd say go for Stanley Lombardo. It's a clean read, it's got excellent notes and guidance, and it's very popular. As a back-up I suggest Robert Fagles.

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A quick comparison of some of the translations I've mentioned, using a passage from book 19 where Achilles receives new arms forged by the gods. (This is the same passage that was used for comparison in a review of Peter Green's translation, which isn't one of the ones I'm recommending.)

Stanley Lombardo:

The Myrmidons shuddered, and to a man
Could not bear to look at it. But Achilles,
When he saw it, felt his rage seep
Deeper into his bones, and his lids narrowed
And lowered over eyes that glared
Like a white-hot steel flame.

Robert Fagles:

A tremor ran through all the Myrmidon ranks -- none dared
to look straight at the glare, each fighter shrank away.
Not Achilles. The more he gazed, the deeper his anger went,
his eyes flashing under his eyelids, fierce as fire --

Robert Fitzgerald:

Myrmidons
began to tremble at the sound, and dared not
look straight at the armor; their knees shook.
But anger entered Akhilleus as he gazed,
his eyes grown wide and bright as blazing fire, ...

Caroline Alexander:

And trembling took all the Myrmidons, nor did any dare
to look upon it straight, and they shrank afraid; but Achilles
as he gazed upon it, so anger entered him all the more, and his eyes
terribly shone out beneath his lids like fire flare ...