The transistor used in the diagram under "circuit for a simple motor controller" is a 2N3904, these are rated at 200mA DC @ 40V.
I don’t see you using a motor that requires over 40V, so current is what we have to be concerned with here.
You should already have the nominal voltage of the motor (i.e. 6V or 3V, not sure what one your using), and now grab a multimeter and find the resistance of the winding on your motor, should be a rather small figure.
Divide the nominal voltage by the resistance of the winding, e.i.
V / R = I (Max Current)
If I is >200mA (0.200) then you will have to use a larger switching device..