I hate to tell ya, but it probably will be stuck with you for a lifetime.
If you get it expunged, it may help, but it still will be uncovered in your background check. Expunged means there has been a significant amount of time since the crime happened, nothing similar has happened since, and there is no likelihood of repeated events.
In Ohio the law is no person convicted of a felony, and then it says "may include expunged cases" so I take that as it isn't necesarily a disqualification, but probably is.
If you are 25 years old by the time you apply, and had no offenses since then, and people the investigators talk to have good things to say about you, you may have a chance.