Technically speaking, your application will require a legitimate date of marriage recognized by a proper authority. This is the date that your marriage was certified, when you were both legally allowed to be married. It is somewhat common for spouses to have their ceremony on a different date then the date when they registered the marriage formally.
As a reviewing officer, divorce dates, ceremony dates and marriage certificate dates are all subject to discretionary review and like any AOS application, you need to make sure your evidence is strong and that your relationship is bona fide. A precise cover letter to organize your evidence is a good idea.
You might want to consider having a firm review your application, many professionals have seen thousands of visa applications between all their employees. This should be negotiated down from full representation if you only want to purchase the time of one employee. For example, my legal assistant is a former USCIS Officer and we could assist you remotely with something like this.
The date on your marriage certificate is the day you became legally married, so that is your wedding date regardless of what you call the ceremony that happened a few weeks earlier. Make sure that this is the date you use on all your immigration forms, to be consistent with the certificate.
My colleagues are correct, the date of your marriage as recognized by a civil authority, the Court House wedding, is the controlling date. But it will cause some confusion and as such I agree with my colleagues suggestion about seeking out the assistance of a qualified immigration attorney in your area.
The statement above is only for general knowledge purposes and at no time intended to be a legal opinion. The individual posting the question and those reading should always obtain the advice of a qualified attorney. No attorney/client relationship is established.