The responses are all on point. Wear a suit if you have one or best clothes available. Be respectful to judge and all court employees. If there were mitigating factors, explain but preface explanation with "I'm not try to excuse myself, but just explain why I did what I did." If you were just being an idiot, well, perhaps say that this is not how I typically drive and I apologize to the court and the public. Do you have any other violations in recent years? If not, you can point to that as example of of driving habits. Look into driving schools for reducing points on license because it may be less expensive than your insurance going up (in response to tickets). Insurance rates may likely still go up, just not as much. I've never worked with traffic lawyer so don't have an opinion.

Re: jail time, you need to have done some serious shit to get jail time and unless you have multitudes of moving violations or negligently hurt someone while driving, it's verrrrry unlikely. If it you had f'd up that much, the cop probably would've taken you into custody right then. My bet is that they took off immediately looking to write another ticket.