Dude I have bee in your shoes many times unfortunately

My advice to you would be this: First of all take it to court no matter what! Its always better to try and get it knocked down or "fixed" than not at all. I know the laws in every state are different as far as reporting goes but here in MN if you get a ticket between 56-64 mph it will not go on your reccord. Also some insurance companies wont even find out if its less than 10mph over the limit.
If I would have known this whenI got my first ticket this year I would have fought my 66 in a 55 so that it wouldnt have gone on my reccord. Go to court and talk to the Prosecuter and see if you can work something out. 66 in a 55 is about the easiest violation to get out of concerning speed and im sure you could get it knocked down to under 10mph or an arrangement that if you dont get another ticket in the next 6 monthes it wont go on your reccord(that was another plea bargin my buddy took in HS.)
Your really not out all that much if you go try and bargin over it. The court will likely not want to waste their time and money over something as minor as this and youll be able to save some $$ and your insurance!
Yeah you should have been driving slower at an earlier time but oh well thats life. Its not like you were doing this in a residential neighborhood and its not like your going unpunished. I'm sure your parents laid into you pretty good and if they were like mine made sure I would never do it again.
It was your first offense and the court will likely go easy on you. Im sure your not going to be tearing around the streets after this incident so theres no loss for them to lessen the charges or let you off.
Insurance for an 18y/o male with a coupe is outrageous and you need to do everythig you can to keep your reccord clean. Its just unfair how they take such advantage of younger drivers. I know their not the best drivers but I have sceen too many poor, older & especially elderly drivers out there and their rates dont get jacked up as high as yours will if you dont get this taken care of. So go to court and Git-R-Done!