If this is your first ticket in quite a while, you might try what I did:

A couple of years ago I was nailed by a Virginia State Trooper for doing 70 in a 55 on a 2-lane road in the middle of nowhere at 9:00 am Sunday morning. Since I was driving a yellow Viper GTS with black stripes and was the only car on the road, I was screwed. Since this was my first ticket in 18 years of driving, I made a court appearance. I was prepared to plead no contest and to offer to attend driving school, in hopes the judge would dismiss the charge. This was exactly what happened -- except that after I plead no contest, the judge asked me if I'd be willing to attend driving school before I could even offer. He even offered to dismiss the BS "no front plate" ticket the trooper had also laid on me. I attended the one-day school -- cost about $75 -- and the charges were dismissed. No points, nothing on the driving record. No way for the insurance company to find out, since the charges are dismissed. I know for a fact this has worked for others. I have a friend who has no qualms about lying under oath, so he gets a phony "miscalibrated speedometer" repair slip, tells a BS story, etc -- but I don't recommend that approach. Since you were less than 20 mph over the limit (20 over in Va is reckless driving), if you've got a clean driving record and were polite to the police officer, the driving school approach should work for you. You will have to pay court costs. Yeah, it's easier to just pay the fine, but the next time the driving school tactic may not work, as you've got a speeding ticket on your record.

I'd forget about the "overpayment" tactic. That's a common old wives' tale, and I'd really be surprised if it works. Every time I read about that, it's never someone saying it worked for them, rather it's "I heard that..." If you decide to go ahead and pay the fine, one ticket should not affect your insurance rates. Of course, all bets are off if you've got other recent tickets on your driving record.