Photo of the area

you need at least a 72" downrod if you want the benefits of the cooling. (clockwise for cooling, counterclockwise for heat. the latter pushes heat down)

make sure the fan you have can sustain a long downrod. some wobble. check w/manufacturer.

19foot tall ceiling is really high for a fan. even with 6 foot rod, you're still 12-13' from the ground.

(6" of rod for every foot is the usually measurement)

Normally from floor to fan is in the 8-9 foot range. not sure how much cooling effect you will get.

you want a ceiling fan made especially for very tall ceilings. not sure if the one you got fits the bill. you need to do some research.

https://www.ceilingfan.com/extra-large

proper height shown here w/a tall ceiling.

https://www.houzz.com/discussions/4016968/ceiling-fans-for-very-high-ceilings

here's a guide

Great information from Beth H. Because you have an adjacent loft area (or is it a catwalk?), also consider the loft ceiling height and distance from the fan so you'll know what you'll be looking at from that angle. It's probably fine, just another consideration.

Have you already figured out the electrical? If you don't already have a fan or chandelier on a switch separate from the overhead lights, you may be looking at work beyond hanging a ceiling fan.

The fan only comes in black, white, or gray, so I selected black to coordinate with your metal balusters. White might seem foreign in this very creamy room.

As an aside, your room has some issues. How in the world do you watch TV in this room. The furnishings layout seems.............strange. If you eliminate the built-ins which just seem loaded with stuff, it could be a nice wall for a much larger scale TV and cabinet below.

The ceiling fan should be mounted at around the surface of your second floor.

Thanks for the comments and suggestions. @BeverlyFLADeziner funny you mention that as we have been thinking on how we do these builtins and if still relevant. We are trying to migrate some of this orange wood out of the home we recently moved into. We have a fireplace right next these builtins as well and currently it has fluted wood and so on around it typical of early 2000's when this was built. I appreciate you putting these images together as it helps with visuals for us. Do you think just opening this wall up with nothing but tv and some lower shelves will make it to bare?

Do you think that the fan will help with efficiency at all with keeping warm air down or will it just go around the catwalk side? Or how about summer too will it feel cooler do you think? I don't want to go through all the work if this is minimal with high likelyhood. I do like the black. The fan i bought is a brushed nickle with wood looking blades but I think I would spray paint them black possibly.

Awkward room. I'd put a conversation grouping in front of the TV.