I think the main point is whether you want an exact translation or a poetic translation.
Lattimore's is the "established" literal translation. I think it's sometime so litteral that the idea gets blurred. You read a Greek verse and then the English one, and you still don't know what it means. His Odyssey is maybe better than his Iliad.
My favorite literal translator is Martin Hammond. It doesn't even try to be poetry, and I agree that sometimes it might be a bit clumsy (though English is not my native tongue). He doesn't translate exactly word for word, but rather tries to convey the meaning, and I think he does very well. If you want a text to help with reading the Greek, this is my suggestion. This is what I use.
A third possibility: Ian Johnston's Homer is very good, and is available free on the Internet (just Google). A bit more "poetic" than the previous two, and so maybe just a bit less exact, but really not much. I think he also tried to make an easier translation, also accessible for younger readers, but this doesn't make it simplistic. Lot's of nice extra material on his site too.
Fitzgerald, Fagles and Lombardo are all not-so-faithful translations. Their main difference is style, not accuracy, and which one is best is mostly a question of personal taste. Fitzgerald's style is quite lofty and elevated, Fagles is more colloquial and Lombardo even more. Personnally I don't enjoy Fagles so much, but the edition is nice with lots of nice extra material. The best thing about Lombardo is that he makes some wordplays that make especially sense if you've already read the same passage in Greek, and that makes him kind of funny to read. But he's no help for understanding the Greek text, I think his text is more a parody of Homer than a translation. But it's a very good parody!