The texbook answer is 38" to 42" .......however the real answer depends on your ceiling height,size of the over all room and the look you wish to achieve. I would suggest using painters tape to gauge exactly where you want your wainscoting....sounds lovely and any room looks better with " bone structure "

Depends on the look you want, but most wainscoting kits usually come in 36 or 48". For ceilings 8-9' its 36" high and for ceilings 10-12' is 48". Some people like to add plate rails so you use taller wainscoting, in that case you cap it 2/3d's way up the wall.

Nowadays they make kits which can be customized on site, companies started to make oversized panels and you can trim them on site to the size you want, and they can be used for heights 37-42", but that requires shaping the panels and priming them on site, and you will need a certain router bit to match the detail on the trimmed side.

think of doing it in 1/3 or 2/3 height rather than half way up which chops the room in half and makes it look shorter than it is.