Double Side Band
Double side band is probably the most familiar to students in Dr. Frohne's Electronics class. This is the type of modulation that the radio was designed for and how signals was taught as well.
The signal looks like or
It makes sense to use this signal to teach how to build a radio because its receiver and transmitter are very simple. All you need is an antenna, a mixer with a cosine wave, a low pass filter matched to the width of the band, and a base band processor (like a sound card). Transmitting the wave would just be the signal mixed with a cosine wave at the desired fc and an antenna.