They don't expect you to have tens of thousands of dollars in your account. In fact, it's not really your account they're concerned with (though showing up with an account $500 in the hole isn't going to help your case). They want to make sure that your fiance/husband can support you until you find work and that he can provide a decent place for the two of you to live. If he has very little in the bank, then he needs to have a letter from his parents stating that they will help you out financially until you get on your feet.
There are people who have gotten their visas with very little in the bank, but if you can help it, it really is best to get some cash in both of your accounts before you apply. Is there anything you'll be selling before you head over? I sold my car right before I came over, so that helped my bank account a lot!
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You'll need to go to the consulate that handles applications from your state. If you got married in NYC or LA, though, I don't think they'd refuse to process your application if you were there in person (you'll need at appointment at NYC). I do know, based on what I've read here, that more people have trouble in LA than at the other two. If you're applying in person, though, I can't see any reason why you'd need to go anywhere other than Chicago. They'll ask for the same stuff at all three consulates--LA just seems to be a bit more nit-picky about stuff.