But it would be best to go to the US and get married there. I don't know for sure but I believe you can't reside in the US with the fiane visa, it just gives you a right to enter the country.
When my sister and her husband were going to get married (she's Peruvian, he's American) the immigrations attorney recommened she travel to the US and while on valid entrance, they should be married, and start the paperwork right away. She got her green card 5 months later, and got a job 2 weeks later. They went through a couple interviews, where they did ask if they slept in the same bed, and if they were together for legitimate reasons. They always kept record of their emails while in long distance and pictures of their wedding, trips together, family gatherings, etc. They never had a problem, and this was in Miami, where marriages for residency are not scarce.
She is now a US citizen and they are doing great, they were married about 10 years ago.
If you get married here, and register the marriage in the US it will take longer. But it is always best to check with an immigrations attorney in the US, and in the state you plan on residing; especially since immigrations laws (and practices) vary with time.