Style of animation comes first. I've gotten into anime, like Hellsing, Daphne in the Brilliant Blue and Mezzo: Danger Service Agency simply on the grounds that the animation style was interesting. Whether or not they turn out to be good depends on a few other things, like quality of the animation and plot.
If the question is just what makes anime great, then the answer is characters. If you cannot think of them as people, and therefore feel the pain, happiness, and other emotions they feel, then its not a very good plot and the character development is poor.
As to what makes anime excellent is the music. If you never notice the music until you've watched it more than one time, then the music is excellent and thereby making the anime excellent as well. That is why any anime with Yoko Kanno or Taku Iwasaki is really good anime.