General District Court
One of the first things you will notice when you go into a General District Court in Virginia is many people to not dress up for court. General District Courts are very informal; the traffic docket can feel like the DMV sometimes.
It isn't necessary to wear a suit and tie, but I recommend that male clients wear nice slacks and a button up shirt. If you are comfortable wearing a jacket and tie, that is fine, but it will almost certainly not make a difference in your case. Judges do not cut people a break because they are dressed in a suit and tie.
For women I also recommend wearing business casual. A skirt or slacks with a blouse or sweater. For both men and women, clothing should not be a distraction.
Circuit Court is much more formal than General District Court. If you are appearing in Circuit Court, I would recommend wearing a jacket and tie. It does not have to be a suit, but if you have a nice pair of slacks and a sports coat, you should wear that. Women should also dress business casual.
It also makes a difference if you're going to court for a jury trial, bench trial, or just a motions hearing. Your attorney will be able to give you good advice, but it's always good to be dressed professionally for Circuit Court.