Basically the size of the wire is limited by the size of the core - which in turn depends on the power required. You want the thickest wire you can use, that will fit in the available space. I would imagine in this day and age they are on-line calculators that will workout all the details you need, or from back in the days of valves simple charts in data books.
Ignore any irrelevance about 'skin effect', which is an RF effect, not really an AF one - and will really do nothing but confuse.
Here's a post (from google) you might find helpful?
Do NOT ignore skin effect if you have a long run and trying to use high AWG gauge wire to save
cost. The calc shows easily 1/2 ohm of Z due to a 100 foot run, 20 Khz. In a 4 ohm system thats
not exactly a throw away consideration. Especially for a real world buyer who buys on specs.
The concepts of skin effect are not confusing for most folks, once explained.
But if its a 10 foot or meter span, 12 AWG, its not a problem. Same if its a one off and your deaf
Also many folks discuss RF as starting at single digit Khz, which is what a lot of people
think is audio, not RF. Its a poorly defined term. There is an IEEE spectrum chart that attempts
to define, but thats just one attempt in many.
In my day job many years ago, I heard of a case where someone ignored skin effect when calculating the wire size required for a long (several km) subsea cable.
The cable was to carry a simple 9600bps modem signal.
The extra loss in the increased frequencies of 9600bps, compared with the previous 1200bps comms, caused some consternation.
I don't know what the final outcome was, I was not that close to the project.
In my day job many years ago, I heard of a case where someone ignored skin effect when calculating the wire size required for a long (several km) subsea cable.
The cable was to carry a simple 9600bps modem signal.
The extra loss in the increased frequencies of 9600bps, compared with the previous 1200bps comms, caused some consternation.
I don't know what the final outcome was, I was not that close to the project.