How high should wainscoting be?
A common guide is about a third of the wall height: 32"–36" for an 8-foot ceiling, 42"–48" for 9–10 feet. Taller "two-thirds" wainscoting (around 60") suits high ceilings and mudrooms.
Board and batten
Smooth panels (or the painted wall itself) with vertical 1x3 battens between a baseboard and a top rail. Space battens 12"–24" apart; matching your stud spacing lets you nail into studs. Example: 40 feet of wall at 36" with battens every 16" takes 6 sheets, 31 battens cut to 27", and six 8-foot lengths each of cap rail and baseboard.
Beadboard
Beadboard comes in 4' x 8' sheets. For wainscoting up to 48" tall, each sheet cuts into two 4-foot-wide pieces, so one sheet covers 8 feet of wall.
Shiplap
1x6 shiplap covers about 5 1/8" per row once the boards overlap. Count rows from the top of the baseboard to the cap, then multiply by the wall length.
Painting it afterward? The paint calculator works out the paint for trim and walls.