Would Nick in Fitzgerald's The Great Gatsby be considered "old money," "new money," or "working class"?

Nick tells us in Chapter 1,

My family have been prominent, well-to-do people in this Middle Western city [unnamed] for three generations.  ... we have a tradition that we're descended from the Dukes of Buccleuch, but the actual founder of my line was my grandfather's brother, who came here in fifty-one, sent a substitute to the Civil War, and started the wholesale hardware business that my father carries on today.

This makes Nick "old money."  His family are "prominent" and "well-to-do."  

However, there are a few caveats.  

For one thing, Nick's family have been wealthy for less than a hundred years.  (His great-uncle started the hardware business in 1851, and this story takes place in 1922.)  Also, their wealth comes from a business, not from an ancestral title or property.  In America, less-than-100-year-old wealth made from a business counts as "old money," but it would not count as old money in England or Europe.  It would be "new money."

Secondly, Nick is from the Midwest, not from the East Coast.  This makes his family (and their wealth) comparatively newer than the rich families of the Eastern seaboard, who may have been there for more than 200 years.  Hence, their way of life is less decadent.  Note Nick's discussion in Chapter 9 about how the East "had always for me a quality of distortion."  

Thirdly, Nick is not living like he comes from "old money."  He comes to New York specifically to earn his living in the bond business (although his father does agree "to finance [him] for a year" to help him get established).   The house he rents is "a weather-beaten cardboard bungalow" between two mansions.  This makes him, compared to Gatsby and Tom, seem almost like working class.