First you need to be aware that obtaining your lawful permanent residency status based on marriage to a USC is a two-step process.
You must first be lawfully married and a civil marriage service, with a state issued marriage license is sufficient. Once you are married, your USC husband must file an I-130 Petition for an Immediate Relative on your behalf. Normally, the I-485 adjustment of status petition is file at the same time, but you are not required to do so.
USCIS makes a decision on your husband's I-130 Petition and if they approve it, then an immigrant visa is made available for you. This decision is based upon the bona fides of your marriage, they are looking for fraudulent marriages solely for immigration purposes.
If you have a visa available, then the next step is to adjust your status. For this process, you must take fingerprints (biometrics) and USCIS checks your criminal background the National Crime Information Center (NCIC). Also, your name is sent to the Department of State for an international background check to see if you are involved in terrorism or other international criminal activity. If you check is clean and your visa is approved, then you can adjust your status and obtain your "Green Card."
Stanley Dale Radtke, Esq.
Law Offices of Haitham Edward Ballout
220 Montgomery Street, Suite 416
San Francisco, CA 94104
In order for USCIS to recognize your marriage, it must be lawfuly celebrated at the location where it occurs. Thus, a civil ceremony is the only requirement. There is no requirement that you have a cultural ceremony in addition.
Since you are in unlawful status you will best be served by consulting with a qualified immigration attorney who can review the facts of your particular situation, recommend a course of action, and answer your questions.