Driving a 4-wire Hard Drive Motor
You could rotate them in any mode you suggested 3 phase Delta or WYE but each is sub-optimal

If you want to run it quietly with optimum torque speed control using synchronous V/F PWM sine wave Voltage control for optimal torque, current and speed control, then you would use them with the HDD spindle driver hardware made for them and drive 3 full bridges in PWM sine voltage.   

Feedback consists of;


a common current sense resistor for all low side driver ground currents to control acceleration
the common wire for BEMF sensing the  balancing of the 3 phases to null any offsets per cycle.