What is the rule of thumb for cable size selection?

It is not that easy. There are several steps to finding the correct cable for a specific load. It largely depends on the type of cable, the environment to be installed and the supply characteristics. Only a trained licensed electrician or electrical design engineer could do this safely. There's no simple rule of thumb. <><><>

As always, if you are in doubt about what to do, the best advice anyone should give you is to call a licensed electrician to advise what work is needed.

Before you do any work yourself,

on electrical circuits, equipment or appliances,

always use a test meter to ensure the circuit is, in fact, de-energized.

IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS JOB

SAFELY AND COMPETENTLY

REFER THIS WORK TO QUALIFIED PROFESSIONALS.