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This is volume 1 of the series you are looking for. There are 9 volumes. The hardcover doesn't have a different ending, it has been retranslated and some feel it gives a different nuance to the end.
The image is reversed, but is this OK?
Barnes & Noble sell the graphic novel
all though the movie is good, it skips stuff adds stuff etc
I would start with Battle Angel Alita Deluxe 1+2
work your way to 3-5
you'll start to see the big differences between the movie and the original Graphic novel.
the story is really amazing, just wish the movie was a bit more accurate.
maybe in the second movie it will stay more true?
Here's the preorder for Vol. 1: https://www.amazon.com/Battle-Angel-Alita-Deluxe-1/dp/1632365987
And for Mars Chronicle 1: https://www.amazon.com/Battle-Angel-Alita-Mars-Chronicle/dp/1632366150