There is not really a 'leave it' mode. You will want to switch occassionally between different modes depending on what you are viewing. Some cable boxes also artificially do things to your image which may make things even more difficult on you.
There is no 'default' and as you likely have seen - when you get rid of the gray bars, you end up with an image that is stretched and distorted, or crops out part of the picture... or both. If you want the cleanest image, live with the gray bars. I personally can't stand it so I put my TV on stretch so it fills the screen and I live with the distortion.
But, when you feed the plasma HD material (actual HD feed!) it will fill the screen entirely. The image will be solid and colors vibrant. Detail will blow you away. DVDs should come close in quality to what HD is, but it will not be HD, just really nice. What aspect to use for HD & DVD? Usually 16:9 is correct. The plasma will liekly auto-configure HD material to fill the screen.
The aspect button is on the remote though because it needs to be used. There is no easy answer to your question, but your preferences will decide exactly how you end up using that button and what aspect ratio you leave your TV in most of the time.
Or, you'll get sick of the aspect button and just watch DVDs and HD material.