What licenses and/or training should one obtain to be able to fly a drone in California? The FAA will open up to flying civilian drones in 2015. Should we get pilot licenses to be ready for this? if so, is there a difference between plane or helicopter pilot license?

Links related: 
NASA Helps Draw Up Rules for Flying Drones in the U.S
FAA making plans for drone flights in U.S.
U.S. colleges begin offering more drone piloting programs to keep up with domestic drone boom
California bills tackle drones, personal privacy
Aviation schools prepare for boom in demand for drone pilots
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.