I think a little darker color on the wall with the window would look nice. Give it a richness.

Would paint work or would wall paper work better?

Do I need to paint all the walls or just some of them?

A greige color would work wonders for the room

Greige is a good fall back color - can't go wrong with it.
https://www.houzz.com/magazine/going-greige-tips-for-choosing-this-all-around-neutral-stsetivw-vs~577375

So greige on all walls or just on some?

What is the room beyond the living room? Maybe start with the living area and then see how the other one looks. Maybe the furniture on that side is ok with the current wall color. Greige sounds perfect!

It almost looks like you are trying to make a decision between the coffee table and the ottoman, with them side by side and not using the rug the same way. The ottoman almost blocks the stairway. If you cannot choose one or the other, can the ottoman scootch back closer to the edge of the couch? In that area?

All walls, particularly if you have an open floor plan. You could do an accent wall if you have a great focal wall if you wanted but its your choice.

My plan is to get rid of the ottoman and put an accent bench instead, but I do not know which fabric to use.

Do you need it for seating? Without anything there, it will look very welcoming as nothing will block the entrance part to the seating. If you need it for seating, I would try for a pattern that has all the colors in that room......the chairs and the pillows.