First of all, your insurance will go up if you get points on your license, that's the basis for raising it. Try your best to lower the amount of points on your ticket. How to do this: first of all, if the ticket is at 3 points or greater, make sure to take the doubling effect in action, take the driver's safety course. This will consist of either 3 meetings of 5 hours or 5 meetings of 3 hours. It depends on your schedule. They are usually once a week. If anything at all, see if the judge will let you take that without having to use the points it gives you, (what I mean is take it for credit, not points), so they can take the points off the ticket without wasting this course option, because you can only take the course once in 5 years.
Then, if the judge says nope, still take the course and drop the point value of your ticket. If you're lucky, it will be a ticket with low point value, making the insurance stay at a minimum.