What are the big red scratch-outs? Furniture you aren't keeping? First step is the couch, second is the rug and third is the paint. Paint color should be based on fabrics and textiles (seating and rug) in the room. It can be custom blended, but the furniture is set in stone. When you shop for the rug, it should be 2-4 feet wider than the sofa. Slip it under the front 1/3 of the sofa and have it extend past the ends by 1-2 feet. You can use painter's tape on the floor to figure out the best size for your sofa and room. I'd replace the dining rug too, so the two are coordinated. In addition, push your TV credenza against the wall and put the TV on a swivel base to adjust for viewing.

I would get a light colored low key rug bigger than the one in the photo. Put the TV where the sofa is now, and the sofa opposite that with 2 end tables. A swivel chair for near the back wall, and maybe an accent guest chair on the side with the tv near the dining room. The arched entry to the dining room limits how "sleek and minimal'' you can be, but you certainly don't have to be old fashioned or cluttered. Everything sen below is from All Modern with other colors available

Your real estate paperwork should have blueprints and measurements of all the rooms, no? Your furniture seems too big for the space you have. Ideally, you could float your sofa where the chairs are, float the chairs to face the sofa, and move the TV to left of fireplace. However, you don't really have a way to get through the living room. Any chance you could return the sofa for two more chairs? This is what's often advised in such small spaces. Paint the entire space a warm white that works with the floors. Get your blues and mustard in there with art work and rugs. You've already made a start. Jan offered a good suggestion to swap the middle space--current dining room--for living room. If you have an attractive eating space in the kitchen--do you?--then a beautiful round table or a long retangular table with casual but upholstered armchairs (less formal than these) could be very inviting as you walk in. Then no problem with walkways. Do a Google search for "switch living room and dining room." Lots of great photos as examples and how to do it. Here's a photo of a front door that opens into dining space. The chest and mirror by the door gives the sense of an entryway along with the hooks.

It looks like the rug is most likely the right size, however we suggest placing the pieces fully on the rug. Currently they are too far apart. You also might consider adding an accent color or some artwork to the space. Notice, how in these designs of ours, the furniture is close enough for everyone to reach the coffee table.