12 AWG Mains Power Cable From Wall To Power Conditioner Sufficient?

Best use 500 MCM copper..............😉

Yes, sufficient. 

I prefer a quality insulated cable. I couldn't hurt. Just don't spend a ridiculous amount. 

Yes of course as said before if it’s on a 20 amp breaker, it’s the same  gauge as what’s in your wall. And sound quality has absolutely nothing to do with that at this point !!

Gague isn't the final defining factor one power carrying ability. Look to your manufacturer for Amp rating and go from there. Depending on what kind of cooper, plated or not, how many strands, how the strands are configured Type and grade of shieling all play a part in they power cables, I would suggest that you decide how many amp you commonly need to provide and  have a cable rated in excess of that. If yo are using a standard 15 amp wall socket then I would want a Distribution box capable of 20+ amp and the power cord possibly capable if 25 amps should be sufficient. Like with your power amp overhead can make or break a sound. The same goes true for power handling capacity in you  'line-in' side.