You can get a head start obtaining your birth certificate (and your husband's), marriage certificate (once you're married), your passport, and husband's DNI. If you'll apply for the visa at the Argentine Consulate in NY you should check with them to see if they have any other requirements. The police records, as Steve said, should be obtained closer to the date they will be used. Birth and marriage certificates as well as police records must be legalized by an apostille (except your husband's, which will be issued in Argentina). All documents must be translated into Spanish by an Argentine public translator. If your passport is plurilingual (US passports are) you won't need to translate it.
As for the police records, it will depend on where you will apply for the visa. If you apply once you are in Argentina, you will need federal records (issued by the FBI), if you apply at the Argentine consulate in NY, you will need police records issued by the local police department of all places you have lived in for the past 5 years.