For simplicity consider making an electromagnet first then progress to solenoids, electric motors, armatures, rotors and stators. A simple electromagnet helps you learn basics of winding and directing EM (electromagnetic) fields. You can salvage parts from old appliances, phones, toys and other projects.
Cost = price of battery.
Wind insulated wire such as copper wire covered with plastic around a soft iron cylinder, called the core. A large nail, bolt or old tool of the correct material works.
Strip the insulation from the ends of the wire. Hold the bare ends to a small DC battery.
Do the ends of the core attract small metal objects such as a paper clip or iron filings?
Once successful, you can add refinements such as switches, a circuit board, and battery pack. Experiment with adding more windings in different patterns, adding more batteries in series or in parallel and gauge the effects on the EM field you created by how it attracts small ferrous metal objects.
Once you master winding electromagnets, you will understand the basics of making motors.