I have actually had this volume, published by Viz Media in 1994, sitting on my shelf since... 1994. After I saw the movie last year, I'm finally getting around to reading this.
Battle Angel Alita is very much the sort of "waifu" character that weaboos have long obsessed over: she's tiny, adorable, has a sweet and spunky personality, and she's also an unstoppable death machine. She falls in love with an ordinary scrub named Hugo for no other reason than that he's a cute teenage boy, and she devotes all of her unstoppable death machine powers to protecting him, saving him, and doing his laundry. (Yes, really.)
If you read Alita's story as a long character arc, this is an important stage in her development. In book one, her ancient, indestructible cyborg body is salvaged by Doc Ito, and she awakens and starts learning about the world. Now, she's starting to have normal teenage girl feelings, but she's still an unstoppable death machine in a cyborg body. Hugo is a dreamer with his own tragic backstory, who aspires to get to the sky city of Tiphares. He's been manipulated by Vector, a shady underworld figure who told him that for a ridiculous amount of money, he could get Hugo there. This is clearly (to everyone but Hugo) a scam, but Hugo has devoted himself to this task for three years, and actually accumulated the necessary money... by doing illegal things, which will eventually lead Alita, a law-enforcing Hunter-Warrior, to a no-win situation.
There's actually a fair amount of character development and tragedy conveyed in this sparse volume, despite it being dominated by pages-long mostly speechless manga battles. While it's YA in theme, the graphic novel is quite graphic, in the style of many manga, with bloody dismemberments, decapitations, eviscerations, crushed heads, and so on. Alita manages to constantly look like a perky cutie even when covered in blood and brains.
If you've seen the movie, then you should know it basically compacted the first three volumes of the Battle Angel Alita manga (including this one) into one story. Volume 1 was Alita's origin story, Volume 2 is Alita's first romance, and Volume 3 is Alita becoming a rollerball champion. We get all that at once in James Cameron's movie, which made it rather "busy," plotwise. I think he was trying to cram too much into one movie, but maybe he was worried that he wouldn't get a multiple-movie arc to tell her story. Possibly this became a self-fulfilling prophecy, given the way the movie tanked.