I'll vote completely in the other direction - either oriental or a trellis or mosaic kind of pattern would give you some color choices to pick up in accessories. A solid color would, IMHO, move this space into the office waiting room danger area.

I think a white, cream, or even light gray shag would be fun. It would lighten the space visually since the floors and seating are on the darker side and would add texture. I'd stay away from non-neutral solid colored shag. I have gray sofas, walls, drapes with a burgundy shag that looks dated after only a few years {was picked to coordinate with an existing element that can't be changed}. If you're not into the shag/flokati look, a fun abstract pattern would be fun. I'd stick with a light background but almost any color{s} would work with the neutrals in your space. It's really a matter of preference and personal style. Good luck...I am in process of buying new area rugs for living and family rooms and it's not easy!

Go with the simple king, I think something too busy might be lost on top of furniture. The space and flow seems to work; it's just no much of floor viewing, therefore you don't need to bring attention to your floor; besides, getting something that will pick u the earth-brown tones might work best.