Where should I adjust first? What would be the most appropriate segment to adjust in order to get the most bang for your buck?
My educated mind would say the area just below your brain must be clear first to allow the full flow of messages from the brain. Logically this is where i would start...  

What does your educated mind say? 
Oh, you think somewhere else?
What do we do now?
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Why not ask the body? The intelligence within each of us knows what is best for the body that it is a part of. Our brain communicated with 70 to 100 trillion cells 24/7.

Question: If the pain is in the Low Back, is the problem always in the Low Back? 

How long before I get better Doc? A loaded question! Most people walking into our offices as chiropractors are considering just one portion of the process. Healing is that part of  the process that is ongoing as is the stresses of life.  Thoughts, Trauma and Toxins continually bombard us daily. The emotional stress of a child being sick,  the chocolate  bar you seemingly can't get enough of,  to sleeping on the couch between trips to pick up the kids from school are things that occur daily. 
     One important thing to note about the above comment is that every minute of your life, your habits either make you stronger or make you weaker. What habits break you down and what habits build you up? No matter the things that make you weaker, make regular Chiropractic Care a habit in your life. Get your Spine checked Often; Maximize Life!