Wire gauge needed for amps

For short runs I would just use what is normally the code for house wiring. For 15 amps that would be # 14, 20 amps #12.

If you use thwn-2 copper wire with 90c devices, then you can go as small as 16 ga

The trick is finding that mythical 90c device. Screw binding terminals are only rated at 60c. (the ones you see on regular switches and receptacles). The "lug" type can be rated 75c but there is not much rated 90c.

That still does not deal with voltage drop and that may be what the OP cares about. A lot depends on the voltage you are dealing with. The voltage drop is a function of amperage and wire size but dropping a few volts at 120v is not the same as dropping that same few volts at

That is what I'd use too. As for the length, it is ok for the size of you house so would be good for 3 feet. When you get to 100 feet or more voltage drop could be a concern.