Generally, claims for personal injury are settled without the need for a trial. In fact, 95% of cases are resolved without a trial. Therefore, I think it is unlikely that you will find yourself in a trial. Your insurance company will provide you with counsel who will handle the entire matter. You will only need to assist him/her with answering written questions (interrogatories), giving your deposition and, if necessary, attending a brief trial. You should relax about the situation and go about your normal business. As far as your rates, they have probably already been impacted as much as they are going to be impacted. The filing of a lawsuit is unlikely to cause an additional increase.
Sounds like you were sued in District Court, which has a jurisdictional limit of $30,000, and the case will be tried before a judge (no jury). The amount being claimed is irrelevant. A judge will decide how much to award. The amount is included simply to cover the highest possible amount allowed in District Court. Plaintiffs sue in District Court on smaller claims because there is a law that allows the admission of medical records and bills into evidence without the need to pay a doctor to come in and testify at trial (which is required in the circuit court, which hears cases with large claims). You/your lawyer can file a jury demand and move it to circuit court. Geico is contractually obligated to defend you -- they will hire and pay your lawyer and will control your legal defense, as they are the ones who will have to pay any judgment on your behalf. Once you are served with the legal papers, make sure you contact Geico and mail them a copy of the papers right away. There are time deadlines that you need to comply with for filing a notice of intention to defend, etc.