Traditionally the stairs should connect (visually) to the main floor colouring. That is to say the areas that guests normally see. I call them the "public" areas. Often times the upstairs are for bedrooms, etc, and are considered "private" and are normally only seen by the family.

I like to see the treads match the main floor colour. And then you can choose either a matching banister or a darker colour (like black) as a contrasting colour. The risers can be a match to the treads or you can paint them a contrasting colour.

A really handsome way to go is to use a slightly darker stain on the treads (like the darkest brown found in the flooring) and then match the banister. And a white riser will finish off the look. White corbels with that look is quite striking.

It all comes down to personal taste. In your situation I would say your stairs should have a strong connection to the main floor colour. The upstairs is its own master.