She has since returned to Argentina, I went and visited her for two weeks, and she is planning on coming to the US again in a couple of weeks.
Option 1: Get married in Argentina, then petition her.
Option 2: Petition her for a K-1 visa, and get married within the 90 day after her entrance to the US with that visa.
You should retain an experienced immigration lawyer to review all the facts, advise you, and handle the case. You can find one through http://www.ailalawyer.com.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
Since she is coming to USA, it is probably faster to get married in the United States. Otherwise, you'll have to wait until you both are in Argentina. USCIS does not accept marriages by proxy until the marriage is consummated, meaning you'd still have to Argentina or wait for her return to USA.
I agree with Mr. Ferrari 100%