I agree with your hunch that a sectional would overwhelm the living room. A standard size sofa on one wall paired with 1-2 swivel chairs. I highly suggest a swivel chair due the the space being dual purpose. It also looks as though a shorter media unit could fit on the wall opposite the sofa. Good luck!

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It's important to use furniture that is appropriate to the size of the space. A sectional sofa would most likely feel a bit overwhelming. I would place a sofa on the wall with an accent chair or two, depending on size, to create a bit of a division. Also, using mirrors can help make the space feel larger. I'd also use low profile chairs like below to keep unobstructed views throughout the space. Area rugs will also help to define each space.

You would want to place the dining room next to the kitchen where it fits logically. To shorten the space, I would recommend two colorful area rugs to define the dining area and the living area, which will give life and warmth. Please don't fall into the gray/neutral groove which is a dying trend that many still falsely think is fashionable. With a colorful rug you can choose a couch and chairs that have pretty colors, not brown or black leather which will kill a room design. Straight, classic lines that won't become dated are best for your furniture because they look good with everything and won't look dated in 5 or 10 years.