How would someone who needs to read a story from A to Z be qualified?
When I'm beginning to watch a movie, or read a book, I tend to want to watch or read the whole story through, even if it is a story of questionable quality or if I know the end. And I don't want to miss a thing. What would be an adjective to qualify such a person like me?
The adjective to describe your not wanting to miss anything might be obsessive, since you are obsessed about reading every word of the book and watching every second of the movie.
How about dedicated or devoted?
In gaming circles, the term completionist is quite popular.