Can you assist me with an interior design question?

Please help, I do not have what it takes for coordinating colors.

I am installing this flooring Canyon Oak in a room that is to become my library. It is not a huge room, about 11’ x 11’. The flooring has a reddish tint, actually a darker red that the photo shows, almost a mahogany.

There will be be built in floor to ceiling bookcases all along two opposite sides of the room. What little of the walls show on either end (one has a door, the other a 6’ x 6’ window) will need to be painted. The door, frame, window sill and trim and the baseboards can either be stained to match the woodwork or painted in a complementary color. I am open to suggestions.

My question is what color should I stain the bookcases? Should they be darker than the floor? Lighter? or perhaps a matching mahogany color? And, since the room is separated from the rest of the house should I match the rest of the home for the paint colors or go with something distinctive.

If I go with your suggestion, I will post pictures of the room (not sure whether this is considered incentive or threat) when completed.