Which power cord to upgrade first?

Your amplification typically will see the biggest improvement in a power cord upgrade. I would recommend giving Frank at Signal Cable a call and discuss your situation with him. You can try his cords for 30 days with a nice return policy.

I don't think there is a "right" answer. In my case I find it to be on the DAC and preamp. My advice would be to buy used and experiment.

Amplifier OR amplifier AND power conditioner (if you're using a power conditioner.) These two cords should be no less than 10AWG wire size. A floating shield (connected at the AC plug end only) is a nice option, but most modern equipment has internal RFI/EMI filtering.

Front end stuff can use smaller gauge PCs, but no less than 14 AWG.
Exception: DACs seem to benefit from larger conductor sizes like 10 AWG. They're not power-hungry devices, so I don't know why this is, it just is.

Any device that has digital circuitry of any kind (DACS, CDT, CDP, HT processors, etc) should definitely have a shielded power cord, and preferably use a circuit that is separate from other (non-digital) front end stuff (tuner, tape, preamp, phono preamp, etc.)

I've never heard a bigger difference than when changing the PC on the source, much more so than the amps in my experience. Obviously, others have heard greater shifts elsewhere. As Wellfed suggests, buy used and experiment.