General Steps (guidelines, formulas and matices) in selecting wire-gauge for copper wires, when knowing the load characteristics?
I believe that one of the best places to start in a situation like this is to refer to existing tables regarding wire gauge and current capacity.  These readily available tables will show many needed details when looking to decide on the best wire gauge to be used.

Some of the details trickle down to negligible (like solder used) when only short wires are used but that assumes you are building in 'safety' margin.  If you are not building in a safety margin, then some of your details become a lot more important.

An example here:

Wire Size Table