Wish I had put more emphasis on cables earlier

Good cables can enable us to realize the potential of the entire system.

Testing in reverse, going from really good cables back to mediocre ones, with lower grade purity metals and poor shielding, while moving them around a system to compare differences can be reconfirming.

Evaluating source components and evaluating speakers with low grade cabling throughout a system can be a great loss of time and less than rewarding experience. I also place a value on cables when the rest of the system and speakers are high in quality. Low grade cables can mask the potential.  ...only as good as the weakest links.

With regards to power cords? How relevant can it be if the a.c. wire from my home fuse box to the outlet is not thick?  Would the amp be most affected by the power cord upgrade? Other than that and my dac, can't change the power cord. 

Yeah. Hate going down slippery slope since this hobby can get really expensive. Haven't really shopped for power cords but are there some reasonably priced ones worth recommending?

@OP,
I, too, was skeptical about power cords. I just bought inexpensive Zu cables and called it a day.
Then I listened to the new AQ cables-speaker, interconnect and power- and became a believer in what cables can do to a system.
Unfortunately, they can become costly.
Though it depends upon your equipment, and budget, I would recommend Audioquest Thunder power cords. They are the least expensive of the newest bunch released and will give you a taste of what a PC can do. They are popping up used nowadays, but I will say these cables are a bit unwieldy, so be sure to add additional length as well as some right angle connectors.
Bob