Any cautions or convictions received before the age of 15 are treated by the US immigration as juvenile delinquency and should not be used against you. If you ever need a police certificate for a visa application, then it will either be disclosed or else listed as "No Live Trace", which means there is something there, but it has been stepped-down
by the police. Your offence appears to be in Category B. For the ESTA application, you will be asked, "Have you ever been arrested or convicted for a crime that resulted in serious damage to property, or serious harm to another person or government authority?" If the answer to that is no, then you don't need to ask us what to do.... The only way your conviction might come to light would be if you were arrested while in the US and the local police felt the need to contact the UK to see if you have a criminal record. If you did apply for a visa, the conviction would be shown, but if it has been stepped-down, it would just say "No Live Trace" and you would then need to follow a process to allow ACRO to confirm whether or not the information you gave the US embassy is correct.
As Chris Stacey said: Although its not formally part of the sentence that is handed down in court, the criminal record that someone comes away with effectively becomes a second sentence, which can have a long-lasting, if not lifelong, impact.