How to select the correct material for wire-wound resistors?
The best wire for a resistor is one that meets its specifications.

The two most important specs for a power resistor are the maximum operating temperature, and the temperature coefficient.

Precision resistors, so current shunts and the like, will require a low tempco. 

Voltage droppers, capacitor dischargers, room heaters, do not require a good temperature coefficient of resistance, but will usually benefit from high temperature operation, as this can reduce their size.

Tying everything together is cost. The earliest resistance wires were binary alloys, nichrome etc. More recently, quaternary alloys have allowed lower tempco wires, at a higher cost. Generally, if you demands higher specifications, you have to use a more expensive alloy.