I've watched minimal anime myself, actually--unless you count all those Battle of the Planets episodes I watched in the 80s. (Still fun, those, but also pretty awful, if you don't have a sentimental fondness for them.)

I think Princess Tutu may be as good an intro as any--I watched Utena before this, which I really liked, but which I think might be a harder way in. Before that--just scattered episodes of Pokemon and Cardcaptors and the like.

Maybe someone with more anime experience would have better ideas.