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. Dont 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. Those who own or have access to an iPhone, iPod Touch, or iPad can download Lexiphanes from the App Store: it contains a searchable version of the complete Liddell and Scott for a mere $3.00 or so.
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.
Sometimes an overview of the text can be helpful: following up on something my daughter did while teaching at Ohio State, I’ve built an overview chart of the Bacchae, which you can view here.