OK, that's a clue.
How do you intend to use the pickup coil? Is it to provide a signal to a switching circuit to operate the motor portion of the motor-generator?
Most pickup coils are small and made with some sort of magnetic core material in the center and wound with very fine wire. It may be possible to find such a coil ready made in an old, surplus relay. Do you have any surplus electronic\electrical shops nearby?
The transformer, or inductor coil, depending on which circuit configuration you intend to use, would be wound to satisfy the step-up ratio needed for the output voltage, and also with heavy enough wire to support the load current demands.
Can you provide a little more detail on exactly what sort of device/devices you have in mind, and what kind of power levels in watts you're looking for?