A speeding ticket of going 15 mph over the speed limit in Virginia can also be termed as reckless driving and is 4 demerit points and a conviction of that offense stays on your record for 5 years.
Failing or disregarding a highway sign is 3 demerit points and the conviction remains on your driving record for only 3 years. All demerit points stay on your motor vehicle record (MVR) for 2 years in VA. General District Court judges in Virginia do not have the authority to adjust or reduce points so it is doubtful going to court would help.
How you might be able to reduce points on your driving record is to earn safe driving points. Safe driving points are assigned for each full calendar year that you hold a valid Virginia driver's license and drive without any violations or suspensions. In some cases, you may earn these points by completing a driver improvement course. You can accumulate a total of 5 safe driving points and may use these to offset demerit points.
As for insurance, not all companies look at driving record points but many instead look at the offense. If you current insurance company does not find the violation to be that serious and it is your first ticket your rates may not be affected. To find out for certain contact your insurance company and ask about their rating system. Or contact the VA Bureau of Insurance, which your insurance company must file their rates with.