Battle Angel Alita, or Gunm, is set in Scrap Iron City and as the name suggests it is a literal dumpster of a place. It's filled with corruption, crime, depression and death. Floating directly above this hell like place is the heavenly city of Zalem. From the little bit of information we do receive, Zalem is a city reserved for the wealthy and educated, but not necessarily 'moral', as we do find out that Zalem often steals bodies and organs from Scrap Iron City and literally dumps all of their waste onto them as well - which, incidentally, is where our story starts!
Ido Daisuke, a doctor and mechanic who lives and works in the postapocalyptic scrapyard, finds the—miraculously preserved—remains of a female cyborg in a junk heap. The doctor revives and rebuilds her and finds she doesn't remember a thing about her past, but she is probably one of the strongest (if not the strongest) cyborg in Scrap Iron City. Her name is Gally. Gally is voiced by the very talented Miki Itou who has also voiced the likes of Android 18 from Dragon Ball and Mineva Lao "Audrey Burne" Zabi from Gundam. You don't get much more bad ass than that.
Gally has a childlike carelessness about her and resonates optimism, a stark contrast from her environment. Gally develops feelings for one of the doctor's acquaintances, Yugo. She learns of his impossible dream to become a citizen of Zalem, the heavenly city in the sky, and finally rid himself of the hell of Scrap Iron City. What follows is a brutal array of trials and tribulations, deceit, psychological anguish and action sequences so tight that you'll forget this OVA came out in 1993.
The music by Kaoru Wada (Princess Tutu) tells the story beautifully and thoughtfully in each segment. The artwork and animation hits superb notes as a lot of the time you don't even need dialogue to know exactly what each character is feeling.
Although this two-part OVA was only intended to introduce the manga to a bigger crowd, I would still recommend it even to the casual anime viewer. That being said, there is a lot of open ended pieces of the plot that are never determined in the adaptation. You're definitely left wanting more, so maybe some manga purchases are in order!