Though there is an astounding range of helpful tools that can be brought to bear on the problem of learning Greek in general, and studying Homeric poetry in particular, much of it is for the more advanced student or the specialist. For this course we will be relying primarily on Stanford’s edition of Odyssey I-XII. The work is neither the most recent, nor the best established text available, but it is sound and the pedagogical leverage it provides is very helpful. It presents a complete set of notes on the relevant passages, with both grammatical and literary discussions.
There are other tools, however, that will prove useful if you can afford them. Some of them are rather inexpensive, for that matter. Some of them are even free.
For your purposes, Smyth will be adequate. We are fortunate that such an extraordinarily good grammar exists in English at such a reasonable price. The next step up is in German, and will cost you hundreds of dollars. Don’t bother with it for now. If budgetary constraints are particularly tight, you can download Smyth as a PDF, since it's now in the public domain.
I strongly encourage every student to have a sound Greek dictionary on tap. For the purposes of this course, the middle-level Liddell and Scott is quite adequate. The larger Liddell and Scott (affectionately known as “Great Scott” by aficianados) has soared to a piratical price of approximately $250. For this course, Cunliffe or Autenrieth will serve, but a more general Greek lexicon is to the point also. On the bright side, however, the larger Liddell and Scott is in the public domain, and hence available for download as a PDF in various locations, and also available in a nifty iPad and iPhone app called Lexidium as well as being part of the offering at Logeion.
As we continue, the zealous team of Project Perseus continues to refine its amazing tools for Greek. Learn to use them. You're good enough at it now that you can get something real out of the experience. They also have both the Middle and larger Liddell and Scott online, with splendid search tools.
There are as many different reasons for making a translation as there are translators, and some are better than others for particular reasons. I generally recommend Fagles’ translations of the Iliad and Odyssey for easy reading; if you want something more accurate to help you crack the tough nuts in Homer, I cannot recommend them as highly. For that task, you might take a look at Richmond Lattimore’s now-classic translation, which preserves with extraordinary fidelity both the literal sense of the Greek and the metrical form Homer used. It is a good deal tougher to read, but it may be the tool of choice there. Don’t, on the other hand, make a habit out of relying on it. It’s never the same as reading the work in Greek itself. Use it only as a last resort.
There are a number of recordings of Classical Greek, including Homer, out there, and fairly few of them really work for me. That's probably largely subjective, but here at least is one MP3 of the proem to the Odyssey to get you started.