Hmmm

Ghost in the Shell as a all encompassing series has 4 movies and 3 "seasons" worth of shows.
--the seasons are : GitS SAC, GitS SAC 2nd Gig, and the "3rd" season is based on the Borders series.
--Borders series culminates in movie #4
**Borders series is kind of set up as a prequel series and movie.
GitS is kind of a stand alone movie.
GitS 2 is another movie following the events of GitS.
GitS SAC and SAC 2nd Gig lead into GitS 3.

If you liked The Matrix, Blade Runner, and other movies that explore the man vs. machine vs. AI philosophical divide you will thoroughly enjoy the entirety of the series as it currently sits.

Saw the teen girl angle after I typed all of this. Hmm the first two movies have a little nudity but no sex. The 3rd and the 4th movie don't have much, if any nudity. The tv seasons don't really do much on the nudity front. No sex scenes in any of it. Now if she has watched The Matrix and Blade Runner and the like.... then violence won't be anything more than most likely what she has already seen.

I would say that Full Metal Alchemist and its successor Full Metal Alchemist Brotherhood are also really solid. Not any more violent than the standard action movie when it has it. The ultra basic set up is the characters use "alchemy spells" to create objects of varying natures. The main story revolves around two brothers who try to use it to bring their mother back but they mess up and one brother gets some souped up appendages and the other has his "soul" transmutated to a suit of armor. The story revolves them trying to get their mom back and how deep the rabbit hole goes with things that tie into other characters and their motivations in the universe, their dad and his own usage of alchemy, and lots of philosophical talk about things. I'd recommend it.

Samurai 7 was pretty darn good. Think of it as a anime inspired remix of Akira Kurosawa's (sp?) Seven Samurai. If you have seen the old black and white original the newer anime version takes nearly the same path but with updated job titles and the "current" anime style.

Cowboy Beebop is great. Lets say its an episodic heist caper series and there is a movie tied to the series too.

Avatar / Legend of Kora are two great series to get into. Avatar is a 4 season long series that is kind of the beginnings of what you get into. The 1 (or 2?) season long LoK series is basically taking where Avatar ended and putting your favorite characters at about 50 years into the future of that universe.