As someone who has just been through all the drama of GC via marrying an American citizen, I wanted to add a couple of points that would be wise to consider beforehand.
Firstly, the initial GC that is issued to you is a "conditional" one, i.e., it is issued on the condition that you remain married to the America citizen for a period of two years at least. The two years however don't count from the date of marriage, but from the date your GC is issued. The average processing time is 6-8 months (currently, things could change by the time you apply next year). You have to provide a lot of evidence that shows that the marriage was entered into in good faith and not just for immigration purposes. So start saving any scrap of paper that has both your names on it-bank accounts, social invites from friends, whatever. I am a pack-rat, and throw nothing away-that helped me put together some evidence of our marriage. When you apply for your conditional GC, you can also apply for an EAD-Employment Authorization Declaration at no extra cost-that usually comes quite soon. That is valid for one year and becomes invalid once your GC is processed. EAD should help you to be considered for at least an internship year.
90 days before your 2 year expiration date on your GC is the earliest time-point you (your spouse actually) can petition to remove conditions and get an unconditional GC that is valid for 10 years. This also requires a lot of evidence to prove that the marriage is continuing in good faith-rental/mortgage agreements, car/other joint loans, beneficiary info., insurance, kids, a whole bunch of stuff. The processing time is again on average 6-8 months in California and Vermont centers and 34 months in Texas (yes, thirty-four, not three to four!), these are the only 3 centers currently. As soon as your spouse and you send in the petition form with all requisite evidence and money, and the cheque clears, they issue a 1-year extension that helps with employment and international travel till your new GC comes through. This letter becomes null and void if your GC petition is denied for whatever reason.
The problem is with GC and long-term contract, i.e., residency situations. I am not aware if you get a yearly contract despite matching into a 3 or 5 or 7 year residency, and renewal is based on performance or whether you are "hired" for the full period, and the yearly review is only to terminate poor performers. In either case, your GC expiring in the middle of residency is a tricky issue. All going well, you should have your GC by Match day for 2013. That effectively leaves only about 18 months in your GC clock for residency before you petition for the removal of conditions. The letter issued once your cheque clears will buy you another year, but until that comes through (and your new GC as well), I am not sure how your program will deal with that. They cannot legally extend your contract. But if for some reason something goes wrong with your application process, and you are denied your second unconditional GC, then the program is left in the lurch as they have to find someone to fill your spot as you cannot be legally hired. I am not saying things will go wrong, but just wanted to make you aware of the worst-case scenario that could happen.
My experience was a mixed bag. I was already living and working in USA for three years before I got married, and living with my husband before marriage for a year prior. So we had some records to show a mingled life before and during marriage. Despite that, we had a very grueling interview before I got my conditional GC. I was quite convinced all this was because we are of different races (I'm Indian, he's Caucasian).
For the unconditional one, I got the 1-year extension letter the day after they cashed my cheque, that helped my contract to get extended for a few months (funding issue). Then they sent me letters asking for more evidence of our "good-faith" marriage though we already submitted everything we had. Apart from rental place and a motorbike loan, we had nothing together, not even a bank account. We sent random things like health insurance bills from when my husband was on my insurance for 1-2 months, photos of us together in various places, photos of joint credit cards we have (only got them for airline miles), etc. I got my new GC without any interview the day after they received this additional evidence. And now I have a full year's contract at my new workplace.
I just wanted to share my experience to make you aware that there are many steps to a GC, and they are expensive, time-consuming and stressful. We didn't investigate any of it before we got married. We never used any lawyer, didn't need one. But an idea of my timelines might help you plan your timelines better:
Entered USA on H1-B from UK-29th Jan., 2006 for 3 years
Married-22nd Aug., 2008
Applied for conditional GC-26th Dec., 2008 (didn't plan on getting one via marriage, PI's funding fell through, he was going to sponsor me)
EAD received-10th April, 2009
Between 30th Jan., 2009 and 10th April, 2009 I was legally unemployable, though I was working and we had funding for me, I could not even be paid retrospectively. I could stay in USA legally though as my case was under consideration.
Conditional GC granted-21st May, 2009
Petition for removal of conditions sent-26th Feb., 2011
1-year Extension received-3rd March, 2011
The extension letter doesn't say so, but the one-year is always till the anniversary date of first issue of GC, 21st May (2012) in my case.
Request for additional evidence from USCIS received-28th May, 2011.
I had till the 8th of August, 2011 to submit more evidence. Some sadness and feeling sorry for myself meant that I didn't do it till 22nd July, 2011.
New GC issued-26th July, 2011.
Hope this helps, good luck.