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

As in most high end audio, it depends. From my experience (50 years) in general speaker cables, power cords, and interconnects. But they are all important and there are many exceptions.

To really get a handle on the sound characteristics and to optimize your system.

First complete your component upgrades… making sure you are completely happy and sure all major components are complimentary and sound great. I use my budget / standard wires: DHLabs. They are good quality and relatively inexpensive… they are my standard for reference. 
 

I get my system broken in… say 500 hours. Based on the sound I will try a few high end speaker, generally Cardas, Transparent, Nordost, WireWorld. I very slowly rotate… a week at least. Listening to music not the equipment. Then amp power cord (AudioQuest Storm Series), then interconnects… and finally power cords to the rest of the system. The process can take over a year… but at the end I have complete confidence in the sound I have. There has been no guess work. I know exactly what each cable has done. 
 

It has taken thirty or fourth years to get this down. It is too easy to be in a hurry to get things over with and make decisions. 

Well i have jumped ship from Brand made power and interconnect cables to diy/parts...and it has been a fun... for most of the experience.As ghdprentice said theres no shoot from the hip in any of this hobby.I replaced amp/cd/conditioner and interconnect cables.Many hours of burn in listening.I did stick with one brand power cables and connectors.

lol...Just did all my interconnects on audioharma/burner... quick 6 hr daisy chained...thought they were done before process...😏.Wow...took them to another level.Try is all i can add...youll never know if you dont.

My belief is that while power can make a difference it may make no difference at all if you have clean power already.

I wrote my thoughts down here:

https://inatinear.blogspot.com/2019/04/power-management-for-frugal-audiophiles.html

Thanks, all. I appreciate learning from you.

Btw .. Companies such as Shunyata and maybe Audioquest are small enough that you can call and speak to some experts.  I found this type of input to be invaluable and quite interesting.