For the first question, it is pretty much a personal choice. The benefit of using the OneCare backup is that it is scheduled via the same interface and if it fails or encounters a problem, OneCare's icon will change color to warn you of an action required. You won't have that with the Vista built-in backup. On the other hand, if you have Vista Business or Ultimate, it adds the capability for a full PC backup, which is not something you can do with OneCare.
For your second question, I have some first -
1. Is this on Vista?
2. What version of OneCare are you using?
3. What is the backup destination you are attempting to use?
-steve