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

Use a subpanel absolutely. Use largest gauge wire to minimize wire resistance and voltage drop for the best results. +1 gs5556. Your weakest link will be the connectors, silver plated high grade outlets.

Awg 10 would be idea Copper, no aluminum wire 
awg8 even better but even high quality Gold copper outlets 
awg 10 is roughly near max .

Okay all, spoke with my electrician. We will be using #1 gauge from the main to a subpanel (I think 150amp subpanel?). And from the subpanel will be using 4x VH Audio 10-2 Cryogenically Treated Romex to outlets.

The electrician also brought up the idea installing a power conditioner at the subpanel. But I wasn’t sure how this would interact with my ability to use a high end power conditioner (e.g. niagara 7000) with my system. Any thoughts on this one? The electrician didn’t have a good answer for me on how an installed power conditioner may affect my system’s power conditioner.

As of right now, I told him to not install a dedicated power conditioner at the subpanel, but still have some time to think about it.

Thanks for everyone's input so far, very helpful!

I assume the power conditioner at the subpanel would work on all 4 lines. What are you intending to plug into the power conditioner in the system room? If you plug the e.g. Niagara 7000 into one outlet then components into the Niagra what’s the point of 4 lines? Or are you going to put a power conditioner at the end of each run  for a total of 4 ? Am I missing something?

#1 wire is a lil over kill but, go with it. Do you really need a 150 amp panel? Just make sure the buss is Copper! I'm happy to see your going to use VH wire. Looks like your on your way. Keep us in the loop.