[pushkins]

You would be very wise to remove the existing plaster especially if it has started to crumble before putting up the new bead board.
The insulation you will need could be anything that would fit without being squashed flat (then ineffective). In most cases R13 batts are ideal BUT in this installation you will not need faced batts.

Installing a vapor barrier will be very ineffective any water spills that hit the barrier will simply run on the barrier and come out in another place, Is there a bathroom above this area ?........are you expecting major spills above this area?

There are many "washes" available for what you are describing have a look at Lowe's or H.D