I haven’t watched a lot of anime, but I will enthusiastically recommend Puella Magi Madoka Magica to nearly anybody. I find it difficult to give a compelling synopsis without spoiling things, but I’ll give it my best shot.
PMMM takes the standard tropes of a Magical Girl Warrior series (e.g. Sailor Moon) and adapts it for an adult audience. And to be clear, this is a show aimed solely at adult audiences; it’s not a show written for children that adults can enjoy. It’s only 12 half-hour episodes, so the investment is low, but it tells a wonderful story in that space. The show features one of the best characterized villains I’ve seen in any media, the artwork is fantastic, and I have no complaints about the quality of the voice acting in the dub.
The central premise is that Kyubey, a cat-like animal who fills the team pet/mentor archetype in the series, seeks out girls with magical potential and makes them an offer. He can grant them a wish, but in exchange they must take up magical powers and fight witches on behalf of humanity. Madoka Kaname and her friend Sayaka Miki will discover that there’s a lot more to the world than the mundane lives they live.
I recommend going into this as unspoiled as possible(for the love of God, don’t google the series), but if that description doesn’t grab you, maybe the following will convince you to give it a try. If you’re already interested, skip it as it is a minor spoiler for an early plot point.
The show is a deconstruction of the magical girl warrior genre. It explores what would actually happen to middle-school girls who were responsible for battling terrible evil.
If you do start watching, make sure that you give it until the end of episode 3. The first couple of episodes lay a lot of important groundwork, but it’s not until the third episode that the story gets going.
The series was collected into a pair of movies, but I don’t recommend them. The first 8 episodes are compressed into a single 2 hour movie, and IMO compressing them like that throws off the pacing (which, other than the slow first two episodes, was very good). The last 4 episodes were expanded a bit to make up the second movie and I feel that the additional material was added in the wrong places and slowed down the pacing at parts where the original faster pace was superior.
There is a true sequel, Puella Magi Madoka Magica: Rebellion, which is divisive but I really enjoyed.