Bedroom back wall + kids bath · one Home Depot trip
List covers both walls. 9 of the 1x4x8s lets the bedroom go 54″ and still leaves the bath. If the bedroom stays 40″, 8 is enough. Pine if you want it to take dings. MDF if you want cheaper and smoother.
13′1″ wide (unless a tight tape says 13′2″) · keep the 5″ base · 10 of 1x4
Nail both corner 1x4s first, measure what’s left, divide by 9, cut a scrap spacer. Don’t trust a guessed gap.
41″ wide · 40″ tall · 4 of 1x4 · 3 hooks
41″ is a clean number: four 1x4s leave three 9″ bays. One hook in each, screwed into the 1x4 rail (not just drywall). About 36″ off the floor is preschool height. If the youngest can’t quite reach, leave the hooks and add a stool for now. Measure the bath baseboard. If it’s not ~5″, batten length is 40″ minus base minus 4.25″ (rail + cap).
4.25″ from one corner. If that’s to the plate edge, you’re fine (~3/4″ reveal). Don’t cover the plate. Pop it to paint. If 4.25″ is to the center, rip that one corner board to ~2.5″.
Level, stud finder, miter or circular saw. No brad nailer? Rent one in the tool aisle.