I take it you didn't have a fiance visa when you got married, just got married on a basic entry clearance? I'll answer your questions on that assumption, but let me know if I'm wrong.

You'll need the following documents:
-Your passport
-His passport (or certified copy)
-The filled-out application form (VAF 2, available at
www.ukvisas.gov.uk)
-The fee
-2 passport-sized photos (take these when you get to the US, I think the size is slightly different than the UK ones and weirdly enough, since it's a consulate in the US (they want US-style photos)
-Your lease agreement (no, if your name has been legally added to this document, you won't need a letter of permission from the letting agent.)
-Marriage certificate
-Pictures, plane ticket stubs, etc. showing that you have met (I wouldn't go overboard with this, when I applied for my fiance visa, they told me all they wanted to see was a couple of photos and maybe some phone bills showing we'd spoken often over a period of time)
-Your husband's bank statements (last 3 months) and paystubs
-A letter from your husband stating his knowledge of and support for your application, and stating that you intend to live together in the UK as husband and wife permanently.
-A letter from you saying the same thing
-The letter from his employer should give the following information: his salary, his job description, how long he's worked for the company, and whether the position is permanent.
-If either of you have been married before, divorce certificates showing you were free to legally marry this time around
As far as your lack of bank statements go, do you have any savings? If it's in cash, I guess you could write a letter to them stating you have 'x' amount of money. If your husband's wage is more than enough to cover your and his outgoings, then they don't focus so much on your savings. Do you intend to work in the UK? It's a question on the form, and if the answer is yes, supply a copy of your resume showing your experience and qualifications.
The only type of letters from family that would help are sponsorship letters, and those basically say "We're aware of Autumn's application to settle here in the UK, we know she's not legally entitled to public funds, and are prepared to assist her financially however we can" and then they have to supply bank statements to show that they can offer said assistance.
Hope this helps, and good luck! You'll get the visa, no sweat.