In the standard PC Cable Wire that goes from the wall outlet to the switching power supply, are they standard and what are the wire specifications? What are the specifications of the three wires inside a PC cable that is used to connect the switching power supply to a US AC outlet.

The positive, negative and ground appear to be the same gauge stranded cable, and I've heard that it can handle 10A, but beyond that I don't really know what the rest of the specifications for the wire are.
Very basically speaking, electricity works like this:


There's some source that delivers a certain voltage.
You have a device that operates at a certain voltage. The device voltage and supply voltage should always match. No, don't put that 120V US device in a 230V outlet in Europe.
The device does something. By doing something it draws current. Most devices also draw some current when not doing anything.
How much power your device draws is the product of these two values:voltage x current = power 


So far, so good. In your case:



  US AC outlet.


the voltage is 120V.
On this other question of yours you linked to this power
supply on amazon. Besides being available gift-wrapped, it
states the following feature:


  You can choose the input voltage (110V/240V) by switch.


110V ≈ 120V, which means the device voltage matches your supply
voltage.
The supply can deliver 30A at 12V on the DC side which means 360W.
If it could transform the electricity ideally, without any
inefficiency, that would be 3A at 120V on the AC side. But your
supply is unlikely ideal. Wikipedia suggests 60-95% efficiency.
Let's be super pessimistic and assume 50%. That means half the power
that goes into the switch power supply is turned into heat. In order
to still get the 360W out, you have to insert 720W. That means
your device draws 6A on the AC side.


What does this all mean for your wire?
What wire size do you need for this supply?

Coincidentally, the above link to the amazon website showing your power supply also suggests the following PC ATX power supplies to me:


Sentey Power Supply 725 Watt
Sentey Power Supply 1000 Watt


Let's get this straight: You can buy a power supply for a PC and plug it into your outlet without even thinking about what a wire size is. You'd just plug and play. That PC power supply will potentially draw more current than the power supply of your 3D printer. A standard wire would be able to supply either one of the PC ATX power supplies linked above and would not have a problem delivering a lower current to the power supply of your 3D printer.

The switching supply doesn't have a plug like a PC ATX supply, but that on its own doesn't make it any less secure (if wired up properly). It's just less common for household appliances.


  Ultimately, I'd like to avoid a fire, or damage to the house wiring.


That's a good and valid concern. 

PC Power supplies deliver 12V and supply more than enough current (like the examples above). They are probably in use in your house already and did neither set it on fire nor damage the house wiring.

A switching mode power supply is just as secure and if bought from a known brand unlikely to do you any harm either if used properly and within its specifications.

Ultimately, this is not a question of secure electricity but a trade-off between secure electricity and the price to pay for it. The standard wire and it's specifications have little to do with this.



Personally, I also use a cheap switching power supply made in china for my printer. It's very noisy and I pull the plug when I leave it unattended.