first, I like wain to go to the existing base molding and then up to where you want it to stop minus the width of the chair rail itself.
Now, when and if you ever want to remove the wain, it will be a huge mess and drywall damage if you glue it. Glue is good, but is permanent.
What I would do is to tack the wain to the wall with paneling nails that are the color of the intended wain and place them only along the seams of the wain. If you have any bowing then by all means place some in the middle to stop this. Not many nails are actually needed since the top will be covered by the chair rail and will be nailed to the studs for good fastening.