One rug per functional area/furniture grouping. So one under the sectional area, for sure. Whether you need another in the other half of the room depends a bit on what kind of function it will have -- seating versus a table, etc.

Here's a color idea - do you have any color in mind yet? Large sectional can take a large and/or textured throw... over the gap at the back... assuming you don't want any slender table in the back.

Super Soft Red and White Chevron and Striped Handloomed Throw Blanket · More Info

Safavieh Bohemian BOH901 Rug 6'x9' Natural/Rust Rug · More Info

"Misty Bridge" HD Curved Steel Wall Art · More Info

100% Jute Hand Knotted Taupe / Aqua Xavier Area Rug by Loloi, 5'6"x8'6" · More Info

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Zimlay Contemporary Bare Tree Iron Set Of 4 Wall Decor 95259 · More Info

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Sangat Kilim Braylen Lt. Blue Rug · More Info

Crystal Chenille Knitted Throw Blanket, Primrose Yellow · More Info

Nut brown option, if you'll have textured items.

Or good with some softened earthy colors - do you happen to like those?

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"Bridge Over Water" HD Curved Steel Wall Art · More Info

A bit much, but it has palette idea - if you'd like the "delicate" lilac, sky blues... and slate blue, cadet blue....

the rug might have enough of creamy-beige to go well with sofa...

Safavieh Suzani Szn312A Ikat Rug, Blue/Multi, 5'0"x8'0" · More Info

Safavieh Suzani Szn376A Ikat Rug, Blue/Multi, 5'0"x8'0" · More Info

I agree with ACM, one rug per area but not just for the sake of adding a rug. Def a rug under the sectional.

What are you planning in the area behind the couch? Play area for little kids, then add a rug. Game table and chairs, possibly a rug but not needed. Your floors are nice! In fact the entire space is very bright and will look cozy after you’ve added a few more pieces and art.

My only suggestion is to consider lowering the tv mount, it looks quite high. You may not even need it if you can sit your tv directly on top of that piece of furniture that’s covered.

We just finished our basement last year - for the walls we found some larger pieces that didnt look puny next to our big sectional (i am a fan of the oversized tapestries from Anthropologie, theyre a steal) we also sprayed a $50 honey oak table/chair set from Marketplace for a game or snack table and that had been a huge hit with the teens