Beautiful open space! If budget is an issue, leaving the staircase carpeted will work well with your flooring selection, it is a neutral colour that will compliment your ambiance I would suggest paining the railing a neutral colour that will not detract your eye from the beautiful flow of your living space. Something along the lines of this colour tone.

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I would paint the chair rail the same color as your walls but in a semi-gloss so they are easily cleaned. Using the same color as your walls will allow the chair rail to blend into the wall.

Your staircase is terrific and has a somewhat "industrial vibe". I would paint it black.