Audio Systems: watts, watt outputs, floor standing speakers

Question
I'm buying an audio system for a small to medium sized house.  I've seen everything from total watt outputs of 16 to 3000.  What is the importance of wattage in terms of quality of sound?  Any system is likely to have adequate volume for what I need, but I sometimes like to listen to classical music loud, and I want good clear sound

Answer
What application are we talking about.  Is this house music (background music) or is this a dedicated listening room?  What type of speakers (brand/model #)?  Are these in-wall speakers, in-ceiling speakers, floor standing speakers?  Give me all the details you have.