Prioritizing Power Cable Upgrades by System Component.

OP, definitely power amp first with emphasis on current. Then (I think) source with emphasis on isolation… shielding. Then in between.

I have upgraded power cables a couple times. About 25 years ago and over the last couple years. Having just made the final decision on the most important component in my system, the amp… I am done for a while. See my User ID for my systems.

So, make sure you got your speaker cables and interconnects dialed in. I think I would then go for the amp… that was by far the biggest difference in no small way for me. You want a high current design. 

it depends on your equipment but think on the order of 10% the value of your component. My amp, for instance cost $22K, and I tested power cords from $800 to $3500… I found that a $1,800 was jaw dropping lay good. You cannot choose exclusively by price. But if you have a $5K component look at the $500 range… and even better look in that range used from UsedCables. 
 

Power cables typically are the last, but really important change that can make a big difference.

“the influence of the power cable is inversely proportional to the quality and sophistication of the built in power filtering and power supply of any component.”

That quote sounds good, makes sense. But my experience definitely does not confirm it, nor at first blush refute it. This would need to be backed up by lots of observations. I can think of lots of possible contra examples from my experience but most are confounded by some factor. But, better sounding equipment is much more sensitive to small differences… so I have my doubts… I would always test.