Is there a handrail on one or both sides? That might help determine the answer.

one side, and it is on the side that will not have the beadboard/wainscotting treatment....

My stairwell (Gothic-revival Victorian house) doesn't just have wainscoating, it IS beadboard. Literally. There's no plaster, just beadboard all the way up. Some of the boards are 12-feet long. It's an unusual treatment and very clean looking, which is nice since it's only 36-inches wide.

If you're going to have a chair rail on the stairwell, make it either higher or lower than the elbow to shoulder zone, or it's in the way.
At handrail height is proper, if on the wall opposite the actual rail; on the same wall as the rail, it obviously will interfere with it.
Casey

sombreul....i'm not sure what you mean by chair rail? we are going to do a beadboard wall treatment going down one side of the steps and there will be some kind of trim molding at the top....the hand rail is on the opposite side....

vivian... our steps are only 38 inches wide with no skirt, just carpeting to the wall...we planned to install a skirt treatment and the beadboard and trim.....i don't think i want to go all the way to the ceiling as it would be over 16 feet at the base of the stairs (which also have a 'turn' one step up from the downstairs floor)....i agree with you i think the beadboard will give a very clean look which will help tremendously with the awful knockdown texture on the drywall....i actually want the beadboard to be high enough that it is above 'eye level' just for that reason...i'm just not sure how up to go