I'm a little late, but I thought I'd add some thoughts, as I am in the middle of the same process.
I was born in 1972 in the US to a British mother and American father, so my situation is very similar to yours. The UK(M) form fits perfectly. All I needed was my birth certificate, my current US passport, my mom's birth certificate, and my mom's expired passport. Your parents' marriage info (mentioned by someone earlier) is not needed when it's your mom who is the British citizen.
Can you make the application without a US passport? I know I sent mine in, but maybe there were alternatives to which I didn't pay attention.
I sent off my application and the documents. In about 2 or 3 weeks, I got a letter acknowledging receipt and stating that the information had been sent to the Home Office for processing. Also enclosed were the documents I had submitted (I assume they made their own copies to send to the HO). That was at the end of April, and I have not gotten my citizenship certificate yet, so it probably will take a little while. But you will get the documents back much earlier, so you don't need to worry about being without them for months.
Once I have the certificate, I'll apply for the passport.