If you "fight it out in court" you will lose unless you can prove to the judge that you were not speeding.
NONE OF THE INFORMATION PROVIDED HERE IS MEANT AS, NOR INTENDED AS LEGAL ADVICE. THE LAW IS CONSTANTLY CHANGING AND INFORMATION DISCUSSED IN THIS BLOG CAN BECOME OUT-DATED WITH THE PASSAGE OF TIME.
If you go to school, the points will be removed and your insurance will not increase. If you go to Court and lose, you will have the points and your insurance may go up. The posted speed limit is an inference as to a "reasonable speed" but you can be going 5 miles over and still be ticketed if the officer testifies that is an unreasonable speed. Your best bet may be to take the school option.