How many different ways can I write "it looked fucking cool"? The phrase "every frame a painting" has become a bit of a punchline, but honestly every still frame or two seconds of animation is gorgeous and iconic.
The story comes across as more complicated than it really is, a hallmark of cyberpunk fiction, when the basic ideas have been rehashed endlessly since RUR, Asimov, and Dick. What makes a person a person? Is there a soul? If there is, where is it, and where does it come from? If every bit of biological data can be reproduced as zeroes and ones, what does it look like if we make a person from scratch? Really, really basic stuff for sci-fi, but presented in a dense and intriguing way.
Every little piece of this builds towards a well oiled, elegant machine. The animation, images, and themes all work on their own, but what gives this film heart is everything in between. The characters are well defined and memorable (countless anime sequels and spinoffs have come out of this), Motoko Kusanagi is like top 5 female anime protagonists, and the relationships between her and the rest of the team keep things interesting. The melancholic score of low-tech traditional instruments contrasts with the futurism of the images, paralleling with the themes of finding soul and humanity amid technology.
The setting implies an urban and population expansion reminiscent of Kowloon walled city (itself a cyberpunk dream made real) and the visual identity of Japan, Hong Kong, and various other Asian locations reinforce themes of globalization and the ethnic stew of the future. The boat ride through urban canals is genuinely one of my favourite sequences of all time: scored by Taito drums, chimes, and a Buddhist choir, the Major catches a glimpse of herself as someone else through a far off window. Rain starts to pour as day turns to night, the sequence finally resting on a fluorescent lit showroom of lifeless mannequins.
This is an adaptation of Masamune "manga pioneer who now only enjoys drawing hentai" Shirow's story, though I'll go ahead and say that most of the magic in this comes from director Mamoru Oshii. His visual style places extreme importance on visual details, the richness of the image presented, and letting the frame of the camera tell the story rather than exposition or dialogue. Yes, there is quite a bit of that still, but not getting hung up on the purposely obtuse writing is the best way to enjoy this.