Puella Magi Madoka Magica is a beautiful story which deconstructs the Magical Girl genre by presenting us with a world where actions have consequences, magic has a price and wishes have strings attached, and all of that is reflected both in the narrative and in the art style of the series.
If I could pick only one anime to recommend to anyone, then I would pick Madoka as the one (including the 3rd Movie) in a heartbeat.
If you are hesitant to watch it, do yourself a favor and just do it.
In-depth:
The series consists of 12 episodes re-mastered into 2 movies (with improved visuals) and a 3rd Movie which is the continuation of the story.
The main differences between the initial series and then the movies is in the visuals, but, since you probably will want to re-watch it, I'd say, watch both, as the series offer more of a psychedelic art-style than the movies, where it is all buffed up, but few scenes lose the crazy in the polishing process.
Story ->
It all begins fairly casual, with a girl being mixed up in a series of events which lead her to the realization that the World is plagued by Evil the regular joes are unaware of, which can only be fought with magic offered to girls willing to enter in a contract with an alien race of cat-rabbit hybrids, an act which even comes with an added bonus of a free wish (practically anything) for the contractee.
It does not take long for the story to deviate heavily from the expectable and typical, by taking us into a psychological and moral journey of the double-edged nature of our universe, where nothing is as it first seem and every coin has both sides.
Everything is accompanied with exciting fighting scenes which are very action packed but at the same time verge on the surreal.
The story is at the same time a love story and a moralizing tale about life.
The characters have to quickly grow up, understand that the outcomes of their actions might not always turn out as they expect them to, that things are not what they seem and that others can lie and deceive to further their own agendas.
On the other hand it is a tale of saving the ones we love, even to the point where its clear we no longer do it for them, but for ourselves.
Add a bit of time travel into the mix and you get a recipe for a S+ title, which Madoka definitely is.
Visuals-->
The art style is very specific, i remember it being off-putting at first, but strangely enticing, nonetheless, when I first started watching it.
It's a mix between hand drawn characters and places and then computer visuals, and experimental mixing of 2 dimensional elements in an otherwise 3D world.
It quickly grows on you, though, and the Perkiness and colorfulness of the Magical Girls is nicely contrasted with the confusing and psychedelic world of the enemy characters.
Every plot twist is accompanied with a specific shift in the surroundings of the character, further underlining the impact of the revelation on the main characters.
Music -->
I think its 10/10. The fights are accompanied by guitars and symphonic orchestra, its there when its needed and gone when its not.
A lot of haunting instruments like violin and cello, electric undertones to contrast with the classic to highlight the tone of the series.
The haunting harmonies of the Kalafina trio makes for an amazing theme song, Magia, which lyrics reveal a lot of the story, but one does not realize that until seen again.
