Cable differences -- power, interconnect, digital, and in what order?

I tend to agree with that:

As in most high end audio, it depends.

But they are all important and there are many exceptions.

For me now everything including power, speaker cable, pre- power amp interconnect, phono interconnects (arm and stage cabling), digital player interconnect, tuner interconnect.

But still it takes patience till you understand what is the effect from every change, what you prefer and can afford.

@hilde45 I’m going to make an assumption you are an experienced listener, your components, speakers and room are on the level to resolve changes in components or cables.
So in my experience…

1. Interconnects

2. Speaker cables (super close second to ICs)

3. Power cables

4. Digital cables

5. Ethernet cables

As to the component to start with on a power cord upgrade? I’d say amplifier first, then power conditioner for your sources, then sources(turntable being very last and I would just use a good stock cord). 
 

@audphile1 Thanks. I'm surprised you put cables affecting the source down at 4, 5 rather than higher.

@hilde45 yes I did - digital and ethernet cables make a difference but they don’t have the same impact as other cables. Think about it…your amp is the last link in the chain before your speakers. Interconnects between your preamp and amp will impact the sound much more than anything upstream including digital and ethernet. Now you need to remove your next bottleneck - speaker cables. And feed the amp good power. 
Now here’s the caveat though…by doing the above you’ll expose other weaknesses upstream starting with your source to preamp cables. Your digital cables aren’t in the picture yet. And if you have a power conditioner for your sources, the power cord feeding it will be next on the list. Then the power cords for sources, then the digital links at the very end. 
Just my thoughts based on my experience. And…it depends on many factors that can change the approach so YMMV as we love to say here.

For me it was not until the majority of my system was up to par THEN I started hearing real differences between different levels of quality interconnect and speaker cables. My ranking is closer to @audphile1, but swapping 3 & 4.