I am a Brit married to an American.
Green card: everything is backed up admin-wise, figure on a good year before you get called for an interview. Get an immigration lawyer, it is worth the money. Your lawyer will advise you to apply for citizenship, this will take 3 years from when then green card is isssued.
Apply for a work-permit at the same time. This will come through in 4 months or so. As soon as you get that, go get a social security card (costs nothing
)
Filing all the paperwork costs $1010 (ridiculous amount of dosh), medical figure another $250-$350 or so (Immigration will give you a list of quacks you can use in your area). My lawyer charged 4K for her time & work. These are New York prices (the 1010 remains the same though).
Hope of some use to you.