Legal Question in Immigration Law in Texas

You cannot remain in the United States legally, solely based upon marriage to a U.S. legal permanent resident. A person is only immediately eligible to "adjust status" (i.e., apply for a greencard) if they marry a U.S. citizen.

If you marry a U.S. legal permanent resident & overstay your visa, you would fall "out of status" (& thus become "illegal"). However, once your spouse becomes a U.S. citizen, you could apply for adjustment of status (assuming you meet the other admissibility requirements, such as no criminal record, among other things).

Your best option is to set a time for a consultation when both the intended spouses can discuss their immediate travel needs and plans and develop an immigration plan from there to best fit your needs. There will be many timing considerations to take into account.

Just to follow up on my previous response to your question, the February 2014 visa bulletin is showing that an approved I-130 petition, filed by a U.S. legal permanent resident-spouse, is only taking about 4 months to become "current" (i.e. eligible to apply for an immigrant visa abroad). So, if your non-immigrant (visitor, etc) visa is expiring soon, or has been expired for less than 180 days, you can leave the country now & your spouse can file an I-130 petition on your behalf. Once approved, & your priority date is current, you can apply for your immigrant visa outside the U.S. (My previous response was just addressing your ability to stay in the U.S. & get a greencard through "adjustment of status").

I hope that further answers your question. Please let me know if you have further questions.