People think that a site finished poly floor makes it "waterproof". Not so. Wood expands and contracts. The only way that you can stop that is to 100% maintain stable 30% humidity levels in your home year round. Even then, with a consumer grade humidifier and AC, you'll get seasonal swings. That means that the wood will not maintain a solid sheet of finish where one board ends and another begins. You will always get cracks in the finish there. Always. You may not be able to see them if you have good humidity control, but they are there. And they will let in moisture. A small amount of moisture if it's only on the surface briefly, but if you let that sit on the surface for a lengthy period, it will penetrate the wood fibers on the edge, and even below, to the sub floor. Just ask any flooring professional. They've been there when the floors that looked undamaged to the homeowner's eyes were removed. And underneath, there was penetration of the moisture, and damage to the wood. And it can be pretty gross on a floor that's been down a while and the owner has had pets long term. If this is a frequent enough occurrence, the consumer will start to see the damage be visible on the surface. The edge fibers will swell, and because they can't swell as much as the fibers would like to, the edge fibers get crushed. That edge crush creates an even bigger gap. That lets more moisture in the next time your pet has an accident there and it sits for half a day waiting on you to get home and clean it up. Vomit is even worse. It's much more acidic. Cat hork will eat away the wood fibers on the edges eventually if it occurs enough at the same spot. And it will damage the poly coating eventually as well. It's hydrochloric acid, pure and simple. Wood floors can be a great choice as long as you do not expect them to remain pristine when you have pets. And you have a contingency plan for dealing with more than the occasional accident. Or you resign yourself to spending a lot of money and then damaging that investment beyond it's ability to recuperate. If it were me, and I am in a similar situation with elderly pets, I'd wait for their passing before putting in new flooring. Some washable area rugs, and vinyl remnants provide a stopgap surface for my oldsters to hork on, and I need not worry about damaging a new investment.

Maybe take a look at Ben Soleimeni rugs? https://bensoleimani.com/ Depending on the size you need, some will come in under your budget while delivering a fair bit of neutral sophistication. (You may remember his name from the work he did with Restoration Hardware) I am also a big fan of the Karastan non wools,like the Euphoria line. Hard to rec without knowing more about your style and how neutral you want to be. For example,is this sort of rug too colorful? https://www.rugstudio.com/karastan-spice-market-mossbrae-vanilla---sapphire-area-rug.aspx Too lively? https://www.rugstudio.com/loloi-ehren-ehr-04-oatmeal---ivory-area-rug.aspx#206569x7__73900

Please show pictures and tell me the dimensions of the room.

Didn't see much that looked "modern rustic cabin" in your ideabooks. However, you should start with modifying the floor plan. I would close both the door and window to the kitchen in the foyer. That will give you a spot to hang a beautiful piece of art or a vintage/rustic textile like a native American blanket if you maintain the cabin vibe. Generally, the foyer should introduce you, your style, and set the expectation for what's to come in the adjoining spaces. I agree, the big window wall is probably supporting and would close up all of it except the width of a regular doorway on the "north" end of it. That will give you a nice TV location on the "south" end of it. If you don't plan for TV in this space and want the breakfast area to serve as dining, then just simply reduce the window to a centered 5' opening. With the breakfast area doing double duty you can incorporate the dining area as a bar for entertaining if you typically serve liquor. Begin with a 3-seat sofa and two chairs, a coffee table, rug, TV credenza, and floor lamps.