You should definitely appear in court on the date of your ticket. It will be your first appearance and they will ask how you want to plead, guilty or not guilty. If you wish to fight the ticket, you can plead not guilty. Pleading not guilty is your right. Depending on your record, you may qualify for a civil penalty or probation (it depends on which court you are in), to keep the ticket off your record and to avoid getting points on your license.
As far as the radar is concerned, if the officer used the radar he or she has to have been trained to do so, and have copies of his/ her certificates, etc. Also, troopers can use a method called pacing to "estimate" a cars speed, and will issue tickets based on that as well. For Careless/Prohibited driving, there is a long list of things under the statute that can trigger that. If you are really concerned about fighting the ticket, speak with a local attorney that is familiar with your Court.