Indeed, "ohayougozaimasu" does also mean "Good Morning." However, "ohayougozaimasu," is the polite form, something you'd use to a respected person. The difference becomes very apparant when you write it out, as it's written using only kana.
"Ohayou" is an interjection, one that means "Good morning." You would use this to a friend, or a commoner. If you were to want to say just "morning," the word would be "asa." Which refers to "in the morning," as opposed to greeting someone.
I must admitt, I wasn't positive, but I consulted my old text book, and sure enough, that's what I found. Not that it really matters or anything, it's just for clarification sake.
As for my favorite of Miyazaki's work, I'd have to say I liked Mononoke Hime the best. Spirited Away was quite good, as was Kiki's Delivery Service.