How Important Are System Cable Upgrades and Where to Start?

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. 

@lalitk is pointing you down the correct path. This journey will take time.

I think it depends on where you are and your timeframe. If your system is all brand new in a new location… that is one thing, if you have an existing system… something else.

I do a system upgrade every 5 - 10 years. I change speakers typically every 10 - 15 years. So, I start with components. I would never start with interconnects or cables… this stuff is highly component / system dependent. I upgrade to the very best and compatible components and listen a lot. Get to know the sound of my upgraded system. Definitely take your time. Nuances mater. 

You have a great power conditioner. I can’t remember if you put in direct lines. These always help… so, whenever you get around to it.

Then, if speakers are new… speaker cables (these can be huge if you have significantly changed your system.. Then power cord for amp. Then interconnects, then the rest of the power cords. At this point your system should be performing really well and time for detailed room treatments.

I would never do components last… it can negate all the work you just did.

“I would never do components last… it can negate all the work you just did.”
@ghdprentice 

I hear you but I hope you’re not suggesting to upgrade components outright without maximizing the potential of existing components?