Agree with this- I'm going through this process right now (the only difference is I'm the US citizen and we're getting married as a result of a normal relationship)- it is fairly simple and most importantly for you- fast.

You get married (can be a civil ceremony- which takes a few hours to arrange), file your paperwork and pay the $1500 fee- in about 2 weeks you receive a confirmation and a short time later you receive a I-94, which gives you permission to work, remain in the US and right of return as long as your application is pending. You then go to an interview to prove that your relationship is real.