Dedicated 20a lines, 125 feet distance, which gauge wire to run?


Want to set up 4x dedicated 20-amp lines for my hifi system. The distance from the outlets to the breaker box is about 125 feet. What wires should I use? 10, 8, or 6 gauge? And should they be solid or stranded? If you could be as specific as possible that would be appreciated (brands, links, etc), as I am out of my depth here. The wire will need to run underground for a good portion, and then into craw space, if that makes any difference.
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The power conditioner at the subpanel would work on all 4 lines, yes. I was planning to have the Niagara 7000 on it’s own dedicated line, with all electronics connected to it. And 2x MC901 monoblocks each on their own dedicated line. So, 3 of 4 dedicated lines allocated.
For me, no Niagara at the subpanel. That's just a bad idea if you have a problem, you'll need an electrician again unless you're handy. Good ideas on the wire, your electrician sounds competent. Silver plated outlets, not gold.  
For the receptacles, I was planning on using 4x Furutech GTX-D NCF(R) AC Receptacles. Is there anything better?
My experience with rhodium plating is it is very pretty but a terrible interface to another surface.

It is too hard to allow for a great grip. Copper alloys, like on a normal wall socket or spade, are soft and deform readily. This malleability makes them deform and make a more complete and tighter connection to another metal. This is something you can readily feel when making a hard to hard surface connection, like nickel to nickel or rhodium to rhodium. It never feels as tight and secure than compared to using a soft to hard or soft to soft connection.

For instance, a nickel plated speaker connector has a very hard time staying tight onto a hard spade. Switch the spade to say gold over copper or the WBT spring loaded spades and the problem goes completely away. I have also used rhodium AC connectors and faced the same problem. They just do not grip or stay in the outlet as well.

The worst high end connector I ever used was a Furutech locking banana. Maybe I got a fake one, but it was just like half a millimeter too small, and the rhodium plating was TOO smooth. It was nearly impossible to make a strong speaker connection. The inexpensive solid copper spades were far superior and a lot less expensive.

Not saying you should avoid Furutech, but all of my experience in various locations (AC/speakers, etc) says rhodium is not very good except to look at.