Bring as much paperwork as you can with you. But, don't volunteer any of it unless you are asked for it. Don't even suggest that you have paperwork with you, just have a small briefcase.
If you don't have certified/attested copies of the disposition from the court, do have copies of secondary documents such as your green card application, the green card itself and any communications about it. It is all DHS, but you are with CBP and the GC is CIS. Bring the court documents which the court could provide. Make certain that they are certified/attested (yes, those can be expensive, but that's life).
There is a decent chance that you won't be asked about the specific incident and if you aren't, don't volunteer. If you are asked whether you have been arrested, answer truthfully "yes". If you are asked for what, answer that. There is no such thing, generally speaking as a "traffic fine". Did you blow through a stop sign or did you mow down 10 children? Be specific and be truthful.
You can't do better than that.
For others going forward and not just for GE, when you have a brush with the law, even if it is minor, it really pays to obtain appropriately certified copies of the paperwork when it is over. People don't because they figure that records are permanent and many court systems charge a small fortune to stick a court seal on a piece of paper.
But, even in fully digitized court systems, things go wrong. It's not just GE, it can be about various security clearances, job prospects, licenses and the like. The one thing you are certain won't haunt you, will.