I'm a bit late to this thread, but here's my 2p:
Madoka is a true masterpiece of anime, but I'd argue that it may not be suitable for a 12 year old as it's rather disturbing - and she'd get more out of it if she watches a few magical girl genre series like Sailor Moon, Magical Girl Lyrical Nanoha, Princess Tutu, etc first. I'd personally save Madoka for a year or two and introduce other things to start off with!
There are anime series for pretty much every genre you can think of. I'd suggest Angelic Layer, my DP reccomends Full Metal Alchemist / Full Metal Alchemist: Brotherhood, which I haven't watched but are very popular and he says they have strong female characters. When I was a teenager, my friends and I enjoyed Revolutionary Girl: Utena, Ranma 1/2, Rose of Versailles and Gundam Wing. If she has other hobbies, there is probably an anime about it that might appeal. For example, Yakitate!! Japan which is a rather daft series about training to be a baker, or Hikaru no Go which is about playing Go (another one I haven't watched).
If you can watch stuff online, Netflix has a growing anime section, or Crunchyroll is an anime-specific subscription service.
If you're not sure about a series, you could try looking it up on myanimelist.net/ to see whether people think it's good and what sort of age rating they suggest. There are also suggestions on each series's page so if she likes one thing you could look up other similar shows she might enjoy.
Don't trust the cover art of manga to tell you what sort of content it contains - have a look for a suggested age range or have a good leaf through first! I've been pretty shocked a few times when leafing through manga at conventions, even after being into it for years. Similarly, don't trust public libraries to know whether a manga belongs in the kids / teenage section or not - I've found manga containing rather graphic pictures of orgies, violence etc marked as kids books because they have cutesy covers and the librarians obviously didn't look any further.
A lot of anime and manga contains significantly more GLBT, crossdressing and (what we would consider) adult content / jokes than our media does, even in media aimed at young kids. I guess this is down to cultural differences as to what we consider suitable for children. :) A fair chunk of anime aimed at girls / young women has rather strongly implied lesbian themes, which personally I think is perfectly OK, but if you think that should be saved for later then you may want to filter more carefully than just based on ratings. :)