For any conviction no matter how long ago or how trivial you will need to go for an interview at an American Embassy. I think parking fines are allowed.
Either London or maybe Dublin. Both have quite long waiting times for an interview so you need to have a lot of time to spare for the wedding but if they give you an visa it lasts ten years. It can be an expensive business. If you get an interview in Dublin they take your passport off you and then the visa and passsport have to be sent to a dublin address. My son in law had real problems as he was fined for not having a tube ticket twenty years ago and they had paid three thousand pond for a holiday. He did get it but it cost a fortune.