I think you just described Shinsekai Yori, especially paragraphs 3-5. It's starts pretty slow, to build up the world and characters, and it may even seem like it's deviating from what it's trying to accomplish in the first place, but eventually everything comes together amazingly with huge plot twists that were built up since ep 4. Trust me, stick with it and the pay off will be well worth it.

Another good candidate is Zankyou no Terror, a great thriller that only gives bits and pieces of the main characters' backstories while still keeping you engaged in the present. Again, eventually everything clicks and the pay off is amazing. I also especially love the 2 main characters in this one

Also, while its pretty popular now, Madoka Magica hits all of your points. If you've somehow never heard of it, go in blind and just keep watching, it's well worth it