Don't forget 'politically important racial and gender demographics' too.
It was a given that whoever Barry picked would be a hardline leftwing pro-abortion judicial activist. After Souter made his announcment Sotomayor was discussed a lot, and I think the view was put forward that she wasn’t as strong an intellect as some of the other people being mentioned...so she may have less impact on the Court than if a more high-powered individual had been selected.