That's a beach house? It looks too beautiful to be a beach house.
I wouldn't do carpet in a beach house. The nature of carpet is that grains will work their way down into it, so that they will not be able to be gotten out, no matter what you do. If you insist on carpet, then the obvious choice is fade-resistant, stain-resistant light colored carpet in the tone of sand. That will show dirt more easily, though. Maybe a two-toned light/dark textured (short plush carpet with textured twisted strands as opposed to straight strands). That is a more casual look that would hide both sand and dirt.
But if it were me, tile with synthetic area rugs would work best. And area rugs that would be small enough to drag outside for airing or cleaning, if necessary. If you must leave wood floors, that would work, as well - with area rugs. Which is what it looks like you have already. If you go with ceramic tile, I don't suggest a tone or color, since that is personal preference, except to suggest something neutral. If you prefer stone-look vinyl tile, you can get those in squares or planks, adhesive or floating.
You have so many options. But I would choose carpet as my last option in a beach house. It would just look so nasty in a short time, I think.
As for natural fiber area rugs, it's my understanding that most natural fibers don't take water very well, so wouldn't protect the underfloor from water, and might stain the natural fiber. If water is an issue. There are probably exceptions, but for a beach house, I'd go with area rugs that can be cleaned easily, taken outside and aired, don't stain easily, have a pattern, etc. That's usu. synthetic.
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Couch?
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