Which power cord to upgrade first?

It might depend on the relative quality of your components. For
example, if you own a Rotel CD player, and an Ayre amplifier, you might
hear greater benefits when changing the amplifier's power cord and vice
versa due to the better power supply and topology of the higher level
component.

As synergy is the key, and as there is no right answer, experimentaion is
important, and if you have one higher grade component than the others,
I'd suggest starting the experiment there.

What components do you have?

Basically any component should benefit from better power cord. The question is - Is the rest of your system good enough to realize the change?
Upgrade power cords(although not all of them) do improve the sound, but the improvement is much smaller than what you would get from IC or speaker cable upgrade.

I think in your case(with a receiver) it's the source that should benefit from a better power cord.
One power cord that I found to work equally good and make a noticable improvement for both digital and analog components is Audience powerChord. It is unshielded, but an excellent cord for either source or the amp. Good luck.

If all your gear uses the same power cord you could just keep swapping until you found the best place for it. Or buy two different cables and do the same.

04-14-06: Audphile1
Basically any component should benefit from better power cord.

Not necessarily true in my experience. I own several upmarket power cords including Purist Dominus and Elrod EPS 3, and I have tried a dozen others. On my $5000 Lamm LL2 Deluxe preamp, the best sounding power cord I have tried is a $5 Volex 17604.

My experience: The source. I use Harmonix Studio Masters. Dedicated line and power conditioner, as well. All for the source. peace, warren :)