Is this your living room pictured here? If so it would depend on the style and design of the room. Being that it faces the street you might want to look at roman shades with the top down bottom up feature so that the light will still come in along with the privacy. Dining rooms I tend to go for drapery unless the room is small.

We recently removed the blinds in our kitchen and nook and replaced them with woven roman shades. We wanted to keep the area bright with a little privacy-most of the time they are in the "up" position. I am a little nervous about keeping them clean; however, I love that I can see light through them (we opted for no liner but you can add a liner or blackout layer if needed)

Keeping out light is the main priority with decor being a close second. This is the only window in the room, and it’s what you see first as you enter—I’d love to find stylish curtains but am not sure where to place a curtain rod with the vaulted ceiling. It’s throwing me off!

Looking at your setup from that second angle suggests you’d have proper clearance on the left but now I wonder about the right side The space on the right is limited by the protruding fireplace “trim” (the mini “hood” above the fireplace opening and the detail below the opening). To see what might work you could purchase a 96” or 104” drapery panel, (whatever appropriate length) hold it up at height rod would be, and see if it hangs ok. Does it look squished, left to right by the fireplace? Does it hang freely? A heavier fabric panel will take up more soace, especially if it’s lined. Maybe a cotton canvas but no lining, or a blackout panel would fit. To help you decide about adequate space, consider the function of the slider. Do you open it a lot? Is that outdoor space a spot you use all the time, or does the door stay primarily closed and youre not going theough that door much. The right panel could hang partially over the door handle (door seldom opened) or it could hang so it fuly clears the door handle (use door all the time). Alternatively, you could mount a shade over the arched window that is long enogh to cover the sliders when shade is let down. (Prob requires a custom made at this length). Whether a shade or drapery, the slider door handle and limited width and height of space will inform your decision as Im sure you already know. Either woud work, but neither are ”perfect”. But perfect is seldom needed. The pros have great advice; maybe they‘ll weigh in