Lets get this shit started!
I just started reading this today
It's a manga series from the 90s, called GUNNM in Japan but called Battle Angel Alita in the states
It has 9 volumes, and a follow up serious called Battle Angel Alita: Last Order (currently ongoing with 16 volumes)
It's about a cyborg who is found by a cybernetics doctor named Ido. She doesn't remember her name, so he names her Alita. Alita at first seems innocent enough, but then shows herself to be a goddamn badass.
So she takes up bounty hunting, and attempts to find meaning in her life by fighting the wicked. At the same time, she really wants to remember her past life