Here's my take on getting the manga to follow the story:
It'll help you understand the basic themes that the movie follows, but it wouldn't explain the plot. Most people tend to look at the movie as a badly compressed version of the manga. It however, isn't. I consider it a retelling of the themes, with it's own original plot (which has been done quite a few times in movies based on longer anime series and manga). I look at them as two different beasts, that share the same characters and overall goal in storytelling.
My suggestion, just watch the movie again. It didn't really sink in with me until the second viewing.
The manga however, is one hell of a read and should be read on it's own merits. Not as some kind of guide to go along with the movie.