In addition to Pharr and Beetham, there is Schroder and Horrigan. I used all three. I would recommend that you use all three--I don't think it matters which one you start with. If you put a gun to my head, I would say that Schroder/Horrigan is probably the single best.
I actually found the Middle Liddel the best for looking up words in Homer, because when I first starting reading Homer, I had to look up so many words that I needed a quick gloss, but I was also interested in what root the words were from. Overall, Cunliffe is a little better than Autenreith, but they are both good.
The best annotated editions are Steadman's. Pamela Draper is great. I found Benner useful, and you can find lots of good old school editions on Google books.
I skimmed through Monroe's grammar, but I'm not a big fan of reading Greek grammar in depth.
Paul is right about the Loebs. The revised editions work well as cribs, but Murray's old versions are written in an archaic English that is sometimes harder to understand than the Greek.
I would think that if you wind up learning Homeric Greek, you will at some point want to learn Attic. The best way to read Homer, once you know Attic, is with Gaza's Attic paraphrase and Apollonius' all-Greek lexicon.
Audio learning is to me essential for mastering a language. These files will get you started:https://www.mtholyoke.edu/courses/pdebn ... 101/audio/
There is in fact no shortage of resources for learning Homer except for one--time. It will take you about two years, spending at least one hour per day (that means if you miss a day the next day you have to spend two hours) before you will be able to read Homer with anything near fluency. Probably five years at that pace before you can REALLY read Homer.
ὁ μὲν χρόνος, ὁ δὲ χαιρός...
I have long wanted to read Homer in the original. Now, the timing is coming for me to make that a reality.