I think I would get one rug, to start, to define the seating area. Though I can’t tell how big an area to cover because I can’t see what’s there where the photographer is standing. Plus it seems a bit odd how the seating area is positioned at an angle.

I get the feeling this home is in the south and beachy. And feminine. So I’d look for a light colored, minimally-patterned rug. The size should take into consideration that it looks like there’s a walkway between the seating area and the piano.

Sketch a floor plan with measurements. Show the area here the sofa is. I don't think placing a rug on an ang;e is going to work.

Is the wall or the sofa on a angle? difficult to tell from your picture but if it's the sofa I'm wondering why. A floor plan with dimensions would definitely help to determine where and what size of a rug is needed. And please post a picture of the wall where you were standing to take the above pictures, we need to see the entire room.

Lots of potential for rugs in this room.

Start with one for the sitting area, as Beverly demonstrated. Just think of ONE.
After it’s in place it will be easier to get complementary ones for the other areas. Stick to a similar style. Modern or traditional?
Trying to find 3 at the same time is overwhelming.

Use painter’s tape on the floor to map out the right sizes. Make sure you pull out the chairs from the dining area and assume walking on the rug with the chairs out.

I need to see the roman shade material since you have already chosen that it will drive the rug choice too. I agree to start with the seating area. I do not like rugs under dining tables and honestly see no reason for one under the pano either . I think better lighting fo sure , a much larger piece of art by the piano . A mirror is best hung when it reflects something worth seeing twice so make sure about that.

You've got a beachy vibe going, I'd think about a seagrass rug.

I think 2 or 3 rugs will be too much, especially given this is your front entry. Instead of grounding areas, they will break up needed visual flow. Add interest/define spaces by adding large art over couch and piano (don’t hang too high). I’d add a simple rug + cushions in LR section to ground it and be sure to tape out different rug sizes to see what will suit best.

With what I see of the room, I also think one rug in the seating area is sufficient. I suggest you replace the wall art with larger more sophisticated subjects.

Here's with one of BeverlyFLADeziner's suggested rugs.