Re: Article: A or the
If it's the very first sentence, then it's up to you. However, "the woman" would suggest to me that the rest of the story/book/novel is going to be based around that woman - it makes her sound important. "A woman" might mean that she is a peripheral character and you are just trying to set a scene in the reader's head. By the same token, "a woman" might later turn out to be very important. In this case, it's really your choice.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.