What licenses and/or training should one obtain to be able to fly a drone in California?
From the second link you posted:


  Until regulations establish who can fly a drone and where, Huerta said, the FAA will license drone operators on a case-by-case basis.


It's doubtful that getting an airplane or helicopter pilot certificate will aid legally with the transition. It could obviously help with the concepts, but until the FAA releases an NPRM (Notice of Proposed Rule Making), the best we can do is guess.