A few thoughts -

First consider your life-style.. on wool, synthetic etc - cleanabililty, staining, wear are very different with different years.

Next (and you did not ask for this) - pull your furniture away.from.the.wall! into a nicer conversational possibility. Yes. Even the sofa can come forward some.. just a bit but away.from.the.wall and certainly the chairs.

Next - I see your puss LOVES the sunshine but she can get it moved to the side of one of those arm chairs. Move the small drum table away from center space. If you need something NOW to 'fill the gap', try the small stack of shelves...w/ lovely LARGER something on to fill in the lower shelves (even the plant that you have on top now)... it's just fine to have the top empty and waiting for your coffee cup. Fill the corner where the little shelf unit is w/ a nice TALL PLANT is a snazzy container.

Now onto the rug - just for a quick try I browsed through HOUZZ on the pages below your post... looked for light furniture, yummy wall tones (like yours and indeed yummy, by the way)...I've screenshot them to focus on the RUGS. What appeals. Any inspiration for you there. Use HOUZZ in a bit of a different focus to send your ideas swirling.

You have such a lovely beginning (although it must certainly seem like a HUGE milestone - and IS - to replace w/ new furniture)... splash away... or reinforce the subtle you've started... rugs, pillows 🤩 (Ohhh PILLOWS) maybe a floor lamp (hmm. A new thought?).

Happy designing. Pam

Owen Rug, Ocean/Camel, 5'0"x7'6" · More Info

Apotema Rug, Gray/Yellow/Orange, 118.5"x78.5" · More Info

One-of-a-Kind Moroccan Hand-Knotted Area Rug, Umber, 8'1"x9'10" · More Info

Kingscote Indoor/Outdoor Handwoven Floor Rug, Kingscote - Apricot, 8'x10' · More Info

I think if you go with a warm colored rug that accent pillows and some decor objects in blues and greens could look nice and bring energy, and surprise to the room, like the decorative art glass piece you have in the window.

Buy your cat a present:

19.7" Round Floor Pillow Soft Seating Cushion,for a Reading Nook OR Bed Room,A5 · More Info

I vote OWEN (the first) from Ital's post

No question over synthetic versus natural, cotton or wool: Natural !

Everything in your room spells Neutral, so just pick Your colors. Then decide Design - classic or modern. Have Fun finding what you like.

Hi. You seem to be wanting more colour for your area rug. You have a painting on the wall at the staircase. That means you liked those colours! I would pull some of those colours from the painting for your new area rug.

You definitely need to add more color with the rug. Perhaps use the colors of the artwork at the left of your photo for inspiration. You can also add colorful pillows. I would put a more substantial end table between the two chairs.

Lay down a sheet or large towel in different colors and you'll get a good idea how to go.

Not sure you need a colorful rug.. you’ve got a very beautiful tone on tone thing going in this room with the natural light from the window… you could go with a natural jute rug and you’d hit a home run in the Hygge design style! Go with it & use throw pillows & accessories to add a little color!

I agree that you have a lovely beginning! I would consider what mood you want to create. Here is my living room, where I was going for a peaceful vibe. (Ignore the child proofing on the end tables and coffee table.) With your neutral furniture, you can add pillows and rug to create whatever kind of mood
you want: peaceful, cheerful, fun, elegant, casual, etc.

Thanks. Really nice and welcoming

Easy breezy! Get two accent colors for pillows. Let your rug have the colors of the accent pillows in them. Niiice....