You have to disclose everything, as mentioned in the prior post. I was informed that failure to do so is an automatic no to the permit. I was advised even sealed juvenile records not disclosed can cause a rejection. It's not fair, what was the point of sealing it, but that's what it is. It might be wise for the original poster to hold off a little while on applying. The longer the time that passes from a "problem" the better. NY is very strange, the application process varies from county to county, and issuance of a permit, in most counties, is up to the sole discretion of a judge. I believe there are counties on Long Island where it is the police department decision. There are rumors of a suit in NY saying current practice violates the constitution, as there is obviously not uniform application of the law.
As far as references go, the better known and respected the reference, the better for you. So yes, school teachers, Doctors, politicians etc can give you an edge. Disclosing to them your violation may (and I only say may) not be necessary, but is probably advisable. Most people, if they think anything of you, would forgive a youthful indiscretion like this.