Calling a guy for a free estimate to scam information is BS. People make their living with their time and nothing more.
Rigid metal conduit is required up 4' because of physical damage. Rocks from mowers, animals, etc. EMT (metal and would be OK) conduit is NOT expensive ... maybe 20 cents a foot.
I would run the line in the attic and then drop straight down on the outside through the soffit (which is not closed in - crummy) down the wall with a 3/4" conduit to an outside weatherproof receptacle (GFI). Then go through the wall to your eq. rack. A #12/3 w/ground (romex is OK) is all you need and run a 220V circuit. Split it at the outside box (11Black/white to outside receptacle and red/white to inside and ground to both. 20 amps is a LOT of power.
Do like I do ... send the wife on the attic crawl part of the mission while you carefully supervise from outside awaiting her arrival at the soffit location! Of course you are responsible for shinning a light in the end to assist her navigation! Actually, I'm ashamed to admit that I just did that 6 weeks ago ... LOL. She did great; I tied the wire to her pant loop so she had both hands free ... hahahaah, I'm so thoughtful. I also let her use my headlamp so she could see, you need that. She is pretty small (comparatively) so it was not too bad .... I would have never made it. It is tight but doable for sure and here in FL it is hot too. I installed a second mini-split into my den and had to get power to it. Be careful as it will be 130° in there and you need to be out in 15 minutes or so ... pick a cool morning , get up early before the sun start to bake it.
Your breaker box is not outside ... it is inside someplace and that is where you will get the power AFTER
the breaker. If you don't know how then do not mess with it - get help. Use a GFI breaker. Attach the conduit with single straps (preferably metal) using Tapcon screws into the stucco/block. One clip every 4 feet or so.
Paint the conduit the same color as the house ... won't be noticeable at all.