I'm not quite experienced in experimental activities......
And I'm not quite sure about the requirements in your school, so I can only provide the following details:
1. design of a home-made DC motor: Please refer to my reply on your another post
2. design of an AC motor: Instead of a pair of permanent magnet, a coil is used instead. When connected to the same source as the motor does, the new coil will produce an alternating magnetic field so that the direction of net torque will remain the same even after the direction of current in the source changes.
3. advantages of AC (=disadvantage of DC):
a) can be easily stepped up and down
b) low loss of power in transmittion (can be stepped up-->power dissipated on cable is lower by P=RI^2)
4. disadvantages of AC (=advantages of DC):
a) easily affected by reactance of wire (compared to DC) because cables are resistive towards alternating b-field produced by AC (Lenz's law)
b) extra components needed on some appliances like motor