I think the "Girl in the Fireplace" has as much heart and ethos as anything in classic Who. "Blink" even as a Dr Where episode is as interesting and fun as anything in classic Who. Personally, I don't think story is an issue. I think it comes down to what people enjoy as far as pacing and acting. The new ones are pretty hyper in story and Tennants acting, but the old ones are often slow and over cheesey. But I don't think story quality tilts one way or the other. By volume the classics has a lot of good stories, but they also seem to have a lot of bad ones too. It comes with the territory of 20 years worth of episodes compared to 4.
Personally I think a newb might as well start with the new series then move to the classics.