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.)