If you apply for an ESTA you will possibly be denied for what you have to answer on the ESTA unless you do not tell the whole truth in which case if they find out you lied you could be banned for 10 years.
Have you tried for an ESTA yet? If denied you can still apply for an embassy Visa and they are dealt with on a case by case basis.
Not sure what nationality you are but Australia does not share court/criminal records with USA on a "State" level only on some Federal levels . Murder Rape or other sex crimes all stay at the Federal level for life even spent convictions so are sometimes shared with USA for obvious reasons.
If your conviction is "spent" and you had no jail time you do not actually have a conviction in UK AU and NZ and need not tell anyone you have a spent conviction or even had a criminal record because it is Spent! Problem is USA doesn't see it that way, even an admittance of "arrest" is seen as undesirable enough to be denied Visa or ESTA, USA doesn't have spent convictions laws! what you tell them is what they then know about you for life.
As others have said do not by a ticket to USA without an ESTA or a Visa as you will be denied boarding the plane and all airlines check because if you arrive in US without authorisation the airline has to take you straight back home at their cost.