Both words have many meanings. Both can be used at the beginning of a sentence and have a similar meaning. Actually, when used in this way ("So, what do you want to do?" "Well, I don't know.") the word so or well does not add any meaning to the sentence; the sentence would have the same meaning without "So," or "Well," to start it. I think there is a small difference, though. I would only use "So," to begin a sentence if I was changing the topic or starting a new conversation.