How Important Are System Cable Upgrades and Where to Start?

Looking at your list, I would start in this order; good luck!

1. Power Source conditioning &/or dedicated circuit

2. Room Treatment: Room selection/ Audio furniture (vinyl playback)/ Equipment placement /absorbers/diffusers

3. Cables with existing components (my preference is to start with Power Cables then Speaker or Interconnect)

4. Component power supply (address those first with wall wart power supply).

5. Component upgrade

Point #3, it’s unlikely that you find any consensus as everyone who believes cable matters have their own methodology. Just ignore the cable naysayers:-)

It somewhat depends upon what you are trying to do.  You would approach putting together a $3k system differently than a $300k system.  Roughly speaking, as you spend more the effects of tweaking become more apparent.  Good loudspeakers and decent room acoustics are fundamental.

I agree with both of the above posts. 

Focusing on cables, I also am in the power cords first camp. I have found that power cords often are component dependent. I suggest buying various used ones to find what works for you and your components.