Im no big fan of anime, though you cant go wrong with anything by Miyazaki (who has been tossing out masterpieces for decades) or Mamoru Hosoda (his The Girl Who Leapt Through Time and Summer Wars are magnificent). Mamoru Oshii though, is quite a different animal since hes proficient in the creation of both animated and flesh and bone films.
Oshiis Urusei Yatsura 2: Beautiful Dreamer (anime) has an ethereal air to it, while his two Patlabor movies (both anime) are more militaristic. However, with Ghost in the Shell, he created an iconic film that explores what happens when an artificial intelligence (that can exist on the web, or inhabit a manufactured body) becomes self-aware.
Set in the dark, violent, borderless 2029 future, cyborgs are used for undercover work. The main character, the beautiful Motoko Kusanagi, finds herself/itself immersed in the search for the mysterious Puppet Master. But theres more to the story than the Puppet Master, or the lush visuals and thrilling action Kusanagi finds herself pondering whether shes really any different than humans since her consciousness (the “ghost), like ours, lives in a shell (in her case plastic and other compounds, while in our case flesh).
Ghost in the Shell made Oshii a superstar, but his next film, Avalon, wasnt embraced in the same manner. This is a live action science fiction film that features an actress who looks very much like Kusanagi in Ghost in the Shell. Some felt it was absolutely brilliant, while others were bored by its very slow pace.
In 2004 Oshii came out with a sequel to Ghost Ghost in the Shell 2: Innocence. In this film Batou, who was Kusanagis partner in the original Ghost, looks for her as he tries to solve the mystery of why sex-cyborgs have been going berserk. Visually, this movie is even more opulent than the first, but once again a slow pace turned off many fans of the original Ghost (which was far more action oriented).
All three films are lovely on the eye, smart, philosophical, and superb. And all three are, in my view, connected.