I'd paint the handrail a soft black/satin finish. Try Benjamin Moore "black panther" . The handrail need not "match" any other trim or the floor. The soft black is timeless.....and modern, and will remain clean forever.

If you want it white or black, replace it with solid surface. You'll never wear it out, it couldn't get any more sanitary, and it will always look great.

The same as the floor

I vote 'same as the floor'. That can be done using a dark stain, or by painting - whichever floats your boat/fits your style/budget. Either way it will work beautifully.