It depends...on the FINAL appearance the stairs are to take. Stringers can be painted...can be veneered...can be stained...so many options. The FINAL design (which you worked out in advance...ahem) will dictate how you finish the stringers.

Without photos or knowledge of what you are TRYING to achieve, there is no way to answer this question. A quick way to figure things out is to figure out what you are doing to the banister and the spindles.

eulerm:

You can't just install wood over your stairs without possibly having to install the same thickness flooring on the first and second floors. There is a reason code only allows a 3/8" riser deviation over a flight of stairs; any more and it ruins the traverser's gait which can have catastrophic consequences.