My understanding is that quality class D audio amps are very difficult to design. I have never seen a DIY version that didn't basically use a pre-built chip or module that did most of the work for them. High switching frequencies are quite hard to deal with, hundreds of kHz being common.
Anyway, for switching apps, I would definitely look at a vertical MOSFET (hexfet, etc) but at high frequency maybe a BJT would be better?
It's easy enough to get the PWM signal from the audio input and a triangle wave generator, but from there it gets HARD. There's a reason quality class D has only come around in the last 5-10 years.