I have three small motors, and I know you should use a motor shield or driver when working with the arduino, but would it be safe to use these with the arduino by themselves without a shield? And if so, what would be the best way to work with them and control their speed?
You will damage the Arduino chip if you connect a motor directly to one of the outputs. I've used the Adafruit motor shield with motors like that.
The Arduino can not drive that type of motor - the start up surge would damage the chip, also a diode is needed to handle the 'back emf' when the motor is turned off.
A servo has internal electronics to switch the motor. you just provide a repeating pulse of the correct length.