I think that Gatsby liked what Daisy represented probably a bit more than what she actually was. Daisy represented "the best" in Gatsby's mind. She was of old money with her marriage to Tom, had discernible taste which was of the best, and presented herself in a manner where she represented the upper echelon of social advancement and fashion. In the end, this is what appealed to Gatsby because it was so opposite of his own life as Jay Gatz. She was not middle class, not banal (from Gatsby's own perception), and not ordinary. Being in love with this vision of Daisy supplanted what she really was and proved to be the hollow foundation of his quest, proving futile in the end.
I would say that there are two major reasons for this. I would say that part of the attraction is simply love. Daisy is clearly an attractive woman, whether in Long Island or when she was younger in Louisville.
But perhaps the more important reason (so I'll say this is my choice for the principal reason) is that Daisy represents what Gatsby aspires to. She is a rich, high class person. Gatsby wants to be in that category. So, when her pursues her, he is showing that he wants to be a rich, high-class person. If she will accept him, then that shows that he has made it.
I am wondering if he is attracted to her also as a part of the chase. She is what he can't have. Sometimes when we are told we can't have something we want it all the more.
When they were teens and had those magical moments together and then had to separate, he had received a taste for something he liked, he really liked. Being told no because of status meant there was potential because status is something that can change. He spied that hope and took advantage of it.
She was a challenge, she was hard to get. Gatsby liked that.