What MOSFET parameters should I look into for this experiment?
You might want to look into using monolithic Class-D Audio Amplifiers for this.

I am not an audio person but there are a few things you need to look out for from a power electronics perspective.

If you pass a sinewave to the gates of your FETs, you're not going to get the same sinusoud out because the FETs wont switch on properly.

You will also need to modulate your sinusoud into a PWM signal suitable for driving the FETs quickly. At this point you will need to add an LC filter to the output to create the sinusoid back from the PWM Pulses.

Shoothrough will also be a concern in a totem-pole output like this where if both FETs are switched in at the same time then you will experience a short to ground which may destroy your FETs and distort the output. Your PWM logic should include deadtime in order to prevent this.

Unless you're interested in building this all from scratch, I would pick up an audio IC to do all this.

If you don't care about efficiency too much, and want to save yourself a bit of pain, a Class-B amplifier might be easier to implement.