So you want to send your kid to one of New Jersey’s top local high schools? That’s great. Just how rich are you? New Jersey’s latest controversial school ratings reflect what research has long shown: Family income is often tied to kids earning higher standardized test scores, helping wealthy communities dominate list after list of the best public schools. Buying in the Garden State towns that boast the best public schools could cost anywhere from $675,000 in South Jersey to more than $1 million in parts of North Jersey, according to an NJ Advance Media analysis of Zillow and state Department o…