I believe Ubercart provides for a default shipping selection these days, but one of our old sites doesn't look upgradeable due to a number of custom modifications a programmer made. So we're looking to see if someone is willing to adapt/provide this functionality for UC 1.0 RC5 release.
To clarify, at the checkout pane, once the customer enters their address, the various shipping options appear for selection, but none are selected by default. The lowest weighted shipping option (first one listed) should be selected by default.
Let us know what it would cost for you to add this!