You didn't specify but I assume you got a court date as opposed to an infraction ticket with an amount that you can pay??
NY is prob different.. but in CT.. plead guilty and pay the ticket = no points. Plead not guilty and you may get a reduced fine but you will get points on your license. Insurance can go up either way for moving violations....depends upon co.
Prior to becoming a cop I got a ticket for 81 in a 65. My insurance co. tried to jack up my rates a year later. Tought me a lesson and made me considerate when giving people tickets.