Damage conversion question

For skills like Frost Blades and Wild Strike that convert physical damage to elemental, and for the Hatred and Herald of Ash gems as well, is it better to select physical damage nodes and support gems or elemental damage nodes and supports? Since frost blades converts 40% of your physical damage to cold, would higher damage numbers be obtained with increased physical damage or increased cold damage? If a character wears a Pyre ring, converting cold damage to fire, which type should be given priority? And if the nodes that increase both cold and fire damage are taken, would the cold damage from the physical conversion be boosted and then the fire damage boosted as well? I was wondering what to focus on for my duelist build.

Thanks!

Converted damage is affected by modifiers to both the source and target damage. So in the case of partial conversion, it's generally better to scale the source type, because that will scale both the converted and unconverted damage. The only exception would be if you could scale the target damage type so high as to make up for what you lose by the source type not being scaled, but this is very rarely feasible.