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

Far better to run a single 50/60 Amp 220VAC line to a sub panel.  You'll have lower voltage drops.  You can then put a balanced 220/120 VAC transformer there.  Noise, voltage, all optimized.

djones514,201 posts09-14-2021 6:58pmIf it's underground it would be the THWN. W for wet. Most #4 is stranded aluminum

Most is, solely due to cost. Copper is probably 5x the price.

Nothing like a pass and a pick six.
Hire an electrical pro and forget about it.

First thing you should do is figure the current draw for your equipment. 
A little overkill is ok but why get carried away?

In a previous job I rewired our ISP buildings with #10 stranded for all 110 VAC circuits, always with a separate neutral (no sharing with other circuits). This was in case we ever needed to change an equipment rack from 110 to 220 (or possibly 208). And yes, stranded handles more current and dissipates heat better.  

Also a common mistake in sub-panels, whether 110 or 220 is bonding the neutral to ground. The is the rule in a main panel but a no-no for sub-panels. 

Where I live it’s illegal to run the four separate lines, so I’d run a 220 line to a sub panel and then run my separate lines from there. It’s also much easier and safer that way.

All the best

JD