For those looking for a heavily philosophical take: obviously watch the original movie, then GITS:2 Innocence and the TV series GITS: Stand Alone Complex.
The 2nd movie is more a work of art than a film. If you watch it, you'll need to have the patience to appreciate that.
The TV series was written by people who wanted a cop drama that happened to feature cyborgs. Not the other way around. Appreciate that and you'll find a lot of interesting ideas presented in a cartoon. I still hold that GITS:SAC presents a better understanding of the Anonymous phenomenon than most techies have today.