Figure out generally what you want the furniture configuration to be, and then choose a rug size that works with it. Then pick furniture that works with the configuration you laid out.

Rug first, because if it has a pattern you can match other upholstery and paint colors to it more easily than the other way around.

Rug first - big enough to place the furniture on it - the furniture should not circle one wood around a central rug.

I was actually advised by an interior decorator that you should always buy the rug first. So it sounds like a great idea!
It's much easier to pick fabric to match a rug than to find a rug you like to match fabric already chosen.

Buy now in a size that fits the room, leaving whatever amount of wood floor that you prefer showing around the edges.

Fine

Is it a mistake to buy an area rug before you furnish the room? I already know that I want to furnish the room based on the color of this rug and it's on sale. But I'm not 100% sure on which size I should get. Would it be foolish to buy the rug now?