I know some people prefer the Fagles translation but Lattimore is my favourite for his sheer ability to convey the full majesty and weight of Homer's phrases without ever making the text unreadable or confused. I read this for the first time as a callow 18-year old student and still go back to it repeatedly for the pure humanity that shines out of Homer's words. In some ways the heroic code of Homer's warriors is alien to us, and yet infinitely understandable still. But what Homer does so supremely is to make his characters live in all their glory and stride off the page from the first words: from glorious Achilles who has to face his own humanity and mortality, to Hector who struggles to maintain his heroic persona in the face of the pleas of his women; from beautiful, self-blaming Helen, to virtuous Andromache, these people really live and suffer and we suffer with them. There is still no moment so supreme in European literature as when Achilles and Priam weep together over Hector's dead body and are reconciled before the end knowing that Achilles own death is fated to follow...
If you haven't read this before then I envy you!