Lots of ways you can go. I could see a linen colored sofa and a camel/caramel vegan leather chair- as just one of many possibilities.

You have very few limits in your room but I'd start with the area rug first and then select the sofa. Leather is always an option.

Can’t go wrong with a neutral shade. Suggest looking on line for inspiration, which might help you decide, as the seating’s color is just the first step in the decor process.

Neutral:

Blending:

Punch of color:

Select rug, sofa, then I recommend chairs in a coordinating color/pattern.

I would not do linen with that wall color but maybe a nice pale green or cream colored sofa . I usually choose the major pieces before a rug and in this case the FP is a big factor too. I might choose a leather sofa to start only becuse it will out last fabric and in a cream color easier to keep clean too. The FP to me is an issue it is heavy looking , the matel not right and IMO does not work with the wall color so a bit torn about a rug choice.. Is this a rental ? I ask because the wall color is driving choices that could be much easier with a different wall color.

Do you really like the paint color?

I would get furniture I like first and then get a complementary color to paint the walls in.

If you do linen and I assume my linen you mean a natural flax color? if that is what you mean then the key to bringing that color in will be to warm it up with all other elements in the space to balance the warm glow of the walls. Find a fabric that balances the coolness of a flax linen and the warmth of the walls and use it as a jumping off place. example would be something like this

notice it has the cool flax color but it also warms it up by using olives and the gold.

another example

and one more

if i walked into this space and you told me you were not willing to paint and you had already ordered a flax linen color sofa but didnt know how to move forward I would do the following

1. dress the windows in a warm woven shade and warm white drapery panels

2 bring in an area rug that combines a natural cooler tan but drives in warmth with olives, browns and golds

3 bring in olive green as a natural compliment to both colorwats

4 find the fabric as mentioned and have pillows made and perhaps an accent piece like cube ottomans or even trim out the inside lead of the drapery panels in it or a coordinating fabric

5 bring in warm rich woods

6 a piece of art that incorporates the new color scheme

but if you have not ordered the sofa I would suggest a cream

If you like this color, I see no reason to repaint. Do you like these colors? Do you have any inspiration pics of what you want a room to look like, regardless of wall color? What other unupholstered furniture pieces do you have that will go in here?

I wouldn't look at matching wall color and upholstery in isolation as there are so many other elements that can bridge the two.

Do you have strong feelings about what rug you want in here? If so, find that first and then get furniture that bridges the rugs and wall color. Remember, you don't have to match the wall color, you merely have to find something that compliments it.

This was on yesterday's House and Garden UK and reminded me of your room. https://www.houseandgarden.co.uk/gallery/hampstead-constable-house-howark-design

The rusty orange lamp, table, and curtains all work together and compliment the wall color. The sage green rug and chairs compliment the rusty orange. The very neutral sofa sort of disappears into it all, which is fine. You can see how just starting with the sofa color would have been the wrong step to take in this room.

Lovely!

Really nice! Love your selections. So many great textures along with the fireplace stone. Please post a pic when you have it all together.

Keep in mind there there is a peach undertone in the paint color and floor stain.