Two things I always consider before watching an anime or reading a manga:
an unusual, or out of this world, or out of the norm, or very detailed plot
the type of characterizations. I'm not a fan of the usual hot-headed, do goody, over-passionate male/female protagonists (although I don't let this be a deciding factor).
Sometimes a third factor might be the animation of the show.
All time Favs. are:
Code Geass series
Darker Than Black series