I have an almost identical bow window in my living room. We did top-down/bottom-up cellular shades (the smallest stock size from JC Penney was a perfect fit, 23"), and then drapes at each end for looks. I didn't want windowsill-length curtains and long ones would have blocked our vents whenever they were closed. And it faces the street, so I didn't want to leave it always open.

Since the room is a living room it will look warmer and homey with some drapes.

We did dark bronze colored automatic shades throughout our home, and our living room window is also large like yours. In our case we could leave it with just the shades, but i think i will probably put drapes or panels too just for softness and color as we have marble floors and no carpets.

You could do a treatment similar to the one in the ref pic for a neutral and casual backdrop

And with the addition with what appears to be solar shades

I should also mention there may be a small table with chairs (for eating) in front of that window ... I like the idea of the top down shades but since it is a small room I'm afraid it my make the room look even smaller BC there will be so many window panels. The room is apprx. 14x15 it will have a couch, love seat, TV and a small table to eat at until the kitchen and sunroom addition gets remodeled in a year or so