The motor you have linked lists 330ma for current so obviously your 300ma supply is not quite potent enough. The driver will allow you to turn down the current supplied to the motor so you don't brown out the circuit but your stepper will see less torque.
The driver accepts up to a 30V supply; a higher voltage sent to the stepper will result in a more responsive stepper. As far as how much current you'll want that will depend on how hot the stepper gets when running. You can allow it to get hot but not so hot that you can't hold a finger to it for a short time.