What type of wire for dedicated 20A AC lines?

Speaking as a former master electrician I would just run 12-2 WG for each line and save the extra money to spend on a good power conditioner. That is all you need.Voltage drops don't come into play until you get around 100 feet runs.

My two cents. Much of what is advocated (large diameter wire, solid copper, etc) is technically **true** but of almost zero incremental value, or, in other cases, "a given" whit US and EU code at least.

I do have a 20A home run from my main panel to a single, quad outlet in my music room.  I do have hospital grade outlets in it (a big $30 or so).  It is 12 gauge (but code demands it  anyway!).  It is copper (but any quality romex or BX is copper). yes you want it off the phase, but why would anyone create a 20A single phase circuit from two? Mysteries abound.

I do advocate a noise filter of some form, a very large isolation transformer or a low pass filter that essentially removes noise. 

Most of these are fairly minor improvements, more a "lack of issues". yes your amp will have a boig power supply and remove much noise.  But the lower the starting point the lower the ending point - all power supplies are filters that can be characterized in dB loss at a given frequency - low in, lower out.  Iso transformers are a trade off - great in theory, but you need to over spec them (i'd say 2 kW) and some general mechanical noise.

This is not about moving more current. That comes from your power supply, either C or LC.  And the current you can move through 14 guage (even 16!) is HUGE relative to what you need.  Code covers the limits already.  Honestly, crap outlets (bad connections) re among the worst problems, along with old, creaky wiring both in and outside your house. Most modern subdivisions are fine.  My public wiring is >70 years old (but meh, still basically fine).

The other BIG DEAL is avoiding ground potential differences (loops). Every single piece of your rig ought to go back to the SAME feed.  Use really good power strips if, like me, you have a dozen plugs.  Minimize the "spanning tree".  Put digital stuff (computers, TVs...) on a different circuit, hopefully ont he other side of a power filter. They represent the noise you are worried about and may have, like spies, infiltrated your room directly - dont look too far, the noise is right in front of you.

Use common sense.

I am not an electrician, but if I was building the ultimate system I would use 2 to 4 gauge power wire fitted through conduit. Would it make a difference in sound, who knows. But I like the idea of having everything overbuilt. You can get a 100 feet of 4 gauge from powerwerx for less than $500. If you are going to redo your internal wiring why skimp? 

I ran #2 wire to a sub panel and then made 2 runs of this stuff:

https://www.gigawatt.eu/produkt/in-wall-cable-gigawatt-lc-y-3x4-mk3/
 

Along with Furutech GTX outlets, this wire has made a very positive impact on my system. It has brought my Coda #16 to life.

       12/2  NM Copper Wire.  Available at any DIY store.  All you will ever need to meet code and run 20 Amps.  Go to 10/2 if it makes you feel good, even though there is probably zero benefit.  You system can only draw so much current and the 12/2 wire has no problem providing more than that.  All this talk about about exotic cables, or going to 8 gague is just noise, and isn't that exactly what you are trying to get rid of?  Would you pay for an 800 HP engine in your car if the local speed limit never exceeded 30 MPH?  Than why would you pay for cable that you will never benefit from.  Maybe this whole argument is becoming a macho "my cable is bigger than your cable" thing?  There's some compensating going on in this thread. 🤣