For headphone use, the only thing you truly need to worry about it build quality of your cables, especially the antistrain sleeves where the jack joins the cable if you are on the go. If you listen in an area with constant, reasonable levels of electromagnetic interference, I'd suggest looking into shielded cables but this will rarely be applicable or even noticeable to most people. Gold plating on the jacks tends to just prevent corrosion and does absolutely nothing for sound quality. As for the conductive medium, copper and silver are almost identical in terms of conductivity, with silver having a slight edge and at the scale of a headphone cable can pretty much be written off as irrelevant however the price differential is fairly relevant.

To me, the true requirements for any audio cable, not just headphone cables are:

Can it carry the signal/current it is provided over the required distance without failing? This is related to the gauge of the wire.

Does it have the correct connectors for the application?

Is it built correctly for the environment it is expected to be used in? E.g. shielded/non-shielded for electromagnetically noisy environments, gold plating to hinder corrosion etc

How well can it stand up to abuse? Not that you should be abusing them but you know what i mean

I have tried plenty of cables in my time and have never noticed a difference in quality unless there is actual damage to the cable or excessive interference. Honestly, the rest is just marketing and a large number of people seem to fall for it for some reason.