As is explained here, "The NYSDMV does not record out-of-state violations committed by NYS drivers in other jurisdictions. The exceptions are alcohol-related violations, drug-related violations, and moving violations committed in Quebec or Ontario."
It's for you to decide whether to plead guilty or fight. You can expect that New Jersey will apply New Jersey points to a New Jersey license if you change your license to that state before the points expire.
You will need to discuss the impact of the ticket on your insurance rates with your insurance agent.

