Linen white is a stock off-white that many people (including myself) love. Ballet white (OC-9) is supposed to be completely neutral and is very light. I think Elephant Tusk (OC-8) is wonderful, but it may be a little too dark for you. It is the same as Ivory Porcelain (239).

I would match the garage door to the roof. No black. No windows, they just increase the grinning face illusion. The black front door is a good idea, but I would use a colonial style. Other colour ideas could include deep plum and burgundy. Your home is traditional, embrace it!

When I think of modern, I always think of black and white. You may not want to paint either section in black paint but what about a light to medium gray? The wainscoting could be painted white and the gray on the walls.

I'd consider the darker gray twill, a rug like the one below (West Elm https://www.westelm.com/products/colca-wool-rug-t1657/?pkey=cpattern-rugs-flooring&isx=0.0.0), and a caramel leather chair. But really, pretty much any colorway will work on those floors. That's the genius of wood and rugs ;-) Decide what you like. And make sure there will be no problem getting the sofa into the space.