I avoid connections like the plague. Nonstop flights only.
In my experience, Virgin America is by far the best airline to use. Jet Blue is also very good. United has stepped up its game recently, but it's still not as good as Virgin. Delta can be OK. I'm usually stuck with them because they have so many available flights and the price point is usually decent.
Not sure about the airports. Of the ones you listed I've only been to JFK.