I was caught contravening a red light in 2005. I was behind a lorry in a roundabout. I wasn't even aware there were traffic lights there until it was too late to stop. My first time in that area and I wasn't used to roundabouts having traffic lights (no roundabouts with traffic lights in my area).

Anyway, I had to pay a fine £60 and I got 3 penalty points on my license.
I think by law you are required to tell your insurance company. I had to renew my insurance anyway that time and when I entered my details for a quotation I realised that the difference between having 3 penalty points on my license cost me £20 extra but guess what.. because I used a new insurance company and therefore becoming their new customer, I got £17 discount so it wasn't too bad.

After 3 years my "crime" will have been spent meaning I will have 0 points again on my license although I will have to keep the record on my license for another year.

I am not familiar with how things are in the US but in the UK, unless the incident was not your fault (e.g in my case if there was a car really close behind me at the traffic light when the light just changed and by stopping immidiately I would have caused an accident), you would not try to challenge your case in court because you will end up paying a greater fine (plus court and lawyer fee) and the same penalty points given to you.

I have regretted my offence (ignorance is not an excuse, I should've realised there were traffic lights there) and for what it is worth I think I have become a better driver since a more careful one anyway.