Did you receive a misdemeanor conviction, or was your case dismissed upon a deferred prosecution? In any event, answer your potential employers' questions truthfully. Get your facts straight about what happened with your case, whether you were convicted and served 30 days, or whether you successfully completed a deferral and your case was dismissed. If the employer asks if you were ever charged with a crime, then the answer is yes, you were. However, it wasn't a felony (based on your question), so if they ask about felonies, you were not charged with a felony. If they ask whether you were convicted (as opposed to charged), answer truthfully. I recommend going to the court and reviewing a copy of your case to determine exactly what happened. Consult with a lawyer about ensuring accuracy on any job applications. If you have a conviction, a lawyer can help you request to have it set aside. Good luck.
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The first answer is very thorough and insightful and I agree with it completely.
But I would just add, as a response to your question "what are my rights?"
Unless you have an employment contract, you can be fired for good cause or for no cause at all (but not for "bad cause" like race, religion, gender).
I think you should first figure out exactly what you have been convicted of, then be completely open and honest with employers. You have no privacy rights regarding this. Indeed, the fact of your conviction is public information easily accessible to any reasonably savvy background checker. So, it's better that they learn about it from you.