Companions and such, however odious their proliferation in many ways is, are very useful, for teachers and students alike. The Oxford Companion makes a differently oriented counterweight to the Cambridge one, and there’s also Powell-Morris New Companion to Homer (meant to replace the Wace-Stubbings classic), harshly reviewed by Janko in BMCR but covering a lot of ground. The new Homer Encyclopedia has been mentioned; that’s a must-have. (I should declare a minor interest in these last two, but I gain nothing from sales. It’s the publishers of these things that rake in all the money.)
Some of the single-author books mentioned are very dated (well, all except Graziosi-Haubold, really). Page is old-fashioned in all respects, and his rhetoric seems tiresome today. (Not that he wasn’t a great scholar.) I’m not surprised that Scribo doesn’t well remember Clarke’s Odyssey book. It’s the least memorable book on Homer I’ve ever read. (I am surprised he commends Griffin; I’d have expected him to damn him as a bloody aesthete; but then I’m only just getting to know you guys.) You’ll be wanting to introduce your students to different critical approaches (you can’t get by without confronting narratology, for instance, and the oral/literate question keeps shifting its dimensions and contours, as does historicity), but the Companions and the Encyclopedia will guide you here, and possibly give you all you need. They’re expensive; just be sure your library has them and you have them on hand. There ought to be a good book on Homeric style, but I can’t think of one.
Some commentators are better than others (I don’t know the Brenner and Seymour ones; Leaf is on Perseus isn’t he?), and of course they’re pitched at different levels. Willcock is excellent if you’re reading in translation, and maybe even if you’re not. I expect you’ll want to expose your students to some really good commentary. Of the Cambridge Iliad comms Janko’s is generally considered the best (a judgment I’d agree with, without putting down any of the others except maybe Kirk’s), and is certainly the most engaging. For the Odyssey there’s the three-volume set by Heubeck and others, internally differing according to individual commentator in a more pronounced way than the Cambridge Iliad set. I’m assuming you can’t count on knowledge of any language other than English, but when it comes to Homer English-speakers are truly blessed. Don’t know what you’re proposing to read, or how much.
I’ll leave it to others to recommend particular books. But Graziosi’s Inventing Homer, not so much about Homer as about “Homer” in the archaic and classical periods, is a breath of fresh air.
You said “Homer and Greek Epic Poetry.” If that’s what you meant, of course there’s Hesiod, the Cycle and other early epic, and the Homeric Hymns, all these now with excellent Loebs by Glenn Most (Hes.) and Martin West (early epic and H.H.), to go no further forward. It’s a lot for a single seminar!