First offense ticket for speeding, should I request PBJ or just pay the fine?

I want to clarify that I am aware I was at fault and have no issue paying the fine, but i've heard a lot of conflicting information and it has me confused. I was coming back from New Castle county, pulled over for going 73 in a 55 by a state trooper. This would be a first ever offense for me, I had never been pulled over before. I believe due to that, he dropped the speed on my ticket from 73 to 60 (only 5 over the limit.). I have no experience in this situation, so I had plans to pay the ticket and go on about it with more caution in the future, but everyone I had informed of this fought that I should request a court date and obtain probation before judgement. The thing is, the officer stated to me that if I did so, he would bring it to my actual speed of 73 in the courtroom. Though, my concern is that if I pay the fine, admitting guilt, my record will be unclean and my insurance will raise significantly. I am NOT on my own insurance plan, either, I am under a family member's insurance, technically driving 'their' vehicle (that I had paid for, but could not legally own as I was a minor at the time of purchase.). I hate to be a bother, but insight would be incredibly appreciated as im uncertain of how to move forward with this.