Fruits Basket - I actually saw the anime first (I don't remember if it was the first shoujo anime I watched, though). I probably share this with many others as a first shoujo.
Most of the early manga I read was not shoujo, because it don't usually like "girly" stuff when it comes to Western fiction. I read a lot of shounen (which I didn't really like) before finding out that I liked shoujo and josei more.