I think round.

I like the round better but either shape only serves 1 seat on each sofa. I would opt for some C tables. And I don't think that oak look goes with your furniture. What is that interesting piece under your TV? It is so cool looking.

Square would be my choice, to help ground the space and for practical/accessible reasons. Try taping out different sizes to see what would work best.

Style: given 3 wood tones - flooring, piece under TV, and bookcases I’d try to complement one of them and head towards contemporary.

https://artemest.com/products/slim-irony-coffee-table

https://www.potterybarn.com/products/palisades-wood-coffee-table/?epik=dj0yJnU9MldhUXpjWDA3Yi1aWE1TR0RBb2dfczlRVDR2Y3lvalomcD0wJm49RmZHR2xnMjBLOWRvZDd3a1RkVHZ1USZ0PUFBQUFBR1pocm5v

Would suggest you pick a finish for the coffee table that will stand out from the other furnishings. If you pick a finish that is too close to the color of the couch it will just fade away.

Thank you so much! greyish tone was an option, but will now take it off the list. What finish would you recommend?

A big ottoman or more is better multiples. Tufted and more solid than soft to take plates and trays and laptops as well as provide comfort to watch programming. Storage will be an added benefit.