DUI trials typically do not involve evidence of a defendant's good character. Good character evidence is more relevant for explaining why you should receive a more lenient sentence after you have been found guilty. You need to consult with an experienced criminal defense attorney to discuss your case.
You need to attend the jury selection because it is a legal summons. As far as a trial for a DUI, those don't involve good character. The sentencing portion (if you are convicted) will involve a statement about your character in regards to the sentence. However, that involves job history and criminal history, not jury duty.
I am a licensed attorney in the state of Nebraska. However, the advice I give here is not to be taken as legal advice. It is merely my opinion based on the limited information given. In order to assure that your legal rights are being properly represented I would always recommend going in for a consultation with an attorney to explain your case in detail and answer any questions the attorney might have.