Best fan for cooling your music room

Vornado. They really do move the air a long way. It will seem like you want a mini, but get the medium size at least, because then you can run it on low. A big fan on low moves much more air for less noise than a small fan on medium or high.
I'm in the same situation and run mine on low far away and sort of behind one speaker where pointed just right I get a really gentle breeze. Adjusted just right it gets my legs and body with almost nothing up at ear level. Perfect. 

I have one of the plastic ones but would go for one of the metal vintage models if buying another. https://www.vornado.com/product-category/circulators-fans

I'm afraid not, I never get on with fans. To me it just feels like they move hot air around. I'd rather use a cool mist spray bottle to keep myself cool, if necessary.

You should try to elevate the boxes a little to allow max airflow. A periodic clean with an air duster or brush will help. Especially heatsinks and tubes.
But take care.

I give my PC a good clean out every 6 months or so just to keep it quiet. The cpu fan can get quite dusty.

Same for my amp every few years, but it's a real pain with all the leads and small screws.

I live in a tropical climate with only ceiling fans.  They're one meter in diameter.  I have them in several rooms.  They are utterly silent.  They are much quieter than any air conditioner I've lived with over my lifetime...including the various full house, rooftop ones.  They provide me with surprisingly effective cooling.

Is your listening room sealed?  Like others have said, a fan will just move hot air around in the same room.  Your audio equipment will definitely heat up the room.  The goal is to move hot air out of the room and cycle new air in.  If you have a door way, maybe a fan in the doorway?  Otherwise, maybe look at your thermastat/AC control.  Some of than have the ability to turn on the air handler to move air without turning on the air conditioner compressor.  This is sometimes labeled as "Fan Auto/On".  Just make sure your thermastat control does not have cooling mode enable when you switch on the air handler "fan".

Vornado's are good, so are Dyson.