What Color Walls With Gray Furniture

Oak trim throughout, dark grey sofa What color for carpet and pain

We are in the process of moving from Wisconsin to Michigan (that's why you see the mess in the photos, as I am here only on weekends to unpack and sort).The woodwork is all oak (orangey-red).

I fell in love with a dark grey, comfy couch, so that is my starting point.We need paint and carpet now.How can I tie together the oak trim and grey sofa?

I thought about a lighter carpet with flecks of grey and brown, then lighted grey on the walls.