I never read the manga but I have just watched the movie and now I'm curious about the next part of story. How does it continue? And, how does the first two arcs (Alita battle angel and last order) end?
The movie ends with Hugo death.
It's hard to compare the movie with the manga because some key points are different, but I will try to summarize.
The main differences in the movie and the manga is that Nova isn't in Zalem, and that the story we saw in the movie is actually 3 stories in the manga.
In the manga the story is divided like this:
story 1: Alita is found and rebuild by Ido (He is from Zalem, no wife or daughter exist/existed). Alita gets the berzerker body and it ends with Alita fighting the big guy from the movie and we get a hint about Nova existing.
story 2: Alita is an experienced Hunter-warrior, and during a raid she meets Hugo. He is a criminal harvesting spines but she doesn't know that. She falls in love, he gets discovered, and the story happens like in the movie. His head gets cut off, he gets a robot body, and he dies climbing to Zalem.
story 3: Alita became depressed after losing Hugo, leaves Ido to join the motorball league. (what is next might actually be a spoiler for an upcoming Alita movie).
She challenges the champion for a fight because of martial artist pride or something, builds a team, and fights the champion in an epic character-defining fight. Another hint to Nova in that he made the champion better with brain altering nano-tech.
After this Alita becomes a hunter-warrior again and crazy stuff happens because of Zappan and his revenge. I can expand on this if you want, but basically a huge fight happens, Alita is forced to work for Zalem to track Nova down and bring him back to Zalem, she meets a bunch of cool people (including a new actually interesting boyfriend), and meets Nova in his stronghold somewhere. Here the story branches into two. The writer became deathly ill at this point and created an ending for the story in case he died. There is a continuation of the story if you ignore the last couple of chapters in the original manga (for anybody reading, after Alita gets blown up by the kid robot, switch to the next manga).
This is basically what happens in the first manga series. The next one is way too complicated to explain in short. I do recommend reading it because it's awesome and the fights become better and grander.