I like it and the door just the way they are. I would not paint any of it, but, if you must, then, leave the handrails the way they are. Painted handrails, show wear quickly, and are a lot of work, to keep up. Stained ones stay nice for years. Black would be my preference if you just have to paint, but, in your house, you have white trim, so therefore, white would be a better choice. White would be better on the door too, if you must paint it.

I agree about not painting any of it. What you have now is low maintenance, but painted wood will not be. Also, please think about future buyers who may not want it painted, especially black.