Reading through, most are probably not mineral rich, the same for QAS, Vogelheim etc.. Too far out (i.e. into Gas Giant country) and the belts will be ice (which is mined, but...). The one that is potentially very rich is the Delta Pavonis rings. That's very interesting, we know there is belt mining on the Chinese Arm from SotFA....
The mineral rich belts seem to be Sol, Clarkestar, Catherine's Star (Henry's Star's companion), Ross 863, and Delta Pavonis, plus potentially others in outpost systems (and Paulo, which isn't exploited yet as per the text).