I love your wainscoting and wall color. Is the wainscoting "real" or is it painted drywall? Also, do you mind sharing your wall color? I would love to see pictures of the other walls in the room. Your DR appears to be a similar size to mine and I never can decide what to put on the other walls.

Ideally allow at least 3 feet for each chair (2' chair depth + 1' to get in and out). So if you have a 12' space, 6' might be taken up by chairs. That means you can fit a 72" round but wouldn't have a lot of extra space. The leaf would make it really tight. I'm all for extra space, but I fell in love with a round table, so I will deal. I have an 8x8 space plus walk room on one side, and I picked out a 48" round table. I have no extra room on some sides but the roundness helps. There are a lot of options. I would go into a showroom and ask the sales associate for help. There are convertible tables, thin pedestals, variable tabletops, exterior and interior legs, 3 legged tables in addition to leafs. Sorry that was probably not much help. I went into a crate and barrel showroom and asked for help and I was able to figure out what I wanted through the process of elimination. They have enough different configurations that you can get an idea of what will and will not work in your space. I would optimize floor space for your family and only add the extra tabletop space when you absolutely have to. The chairs make a big difference in how much space you have around the table when not in use. You can choose uncomfortable chairs that fit tightly against the table (if the table allows) or comfy upholstered chairs that take up more space when pushed in as much as possible. If you go rectangular, you have the option of benches. They have upholstered benches too. Every inch matters. If you can trim a few inches off the chairs or table edges or scooch the chair under the table a bit more, you may be able to come up with another 6-8" around the table. This one says it will fit 6-8, but I wonder if you could get more kids around it if you use benches. (It's not the most attractive IMO.) Table goes from 34x57 to 57x68.

We have a dining area that is similar in size (12x15), however, ours is open to the kitchen on the 12' side. We have a 84" table and I think it fits the space very well, while still allowing for easy traffic flow around it. I think that a table that is permanently 96" might feel a bit large, especially if you're considering larger host chairs.

Keep the rectangle. It looks nice. A round table for six is really big and if you try to do any other work on it - like using it as a temporary desk or crafting area, it is hard to "spread out" on a round table. Also, a round table big enough for six makes it hard for guests to reach the serving dishes in the middle. Is there room behind the sofa to use the console like a sofa table. You could keep some art on the wall , but move the table closer. Although, I don't think it looks crowded. Maybe just pushing things around a bit to tweak the distances and relocating smaller items. Is there room to rotate the dining table so it is parallel with the console? One more thought, place mats and table runners are much easier to use on a rectangular table. Nice condo. You have good taste.