HELP, please! How do I attach this?

Hello, I'm new to woodworking, and I don't have a lot of experience with the use of different sheet goods. I'm trying to remodel a rail car and put coffered boxes up along the center of the ceiling. I was planning to make the boxes with 1 x 4 pine boards for the sides and 1/8" masonite/hardboard on top. The boxes will be about 3' x 6'. Would the masonite need to be reinforced on the back so that it doesn't bow, and what's the best way to attach the masonite--dado the pine boards, glue & nail, or glue & screw? Should I use plywood instead, and if so, what thickness? I'm planning on painting the boxes to match the tin ceiling, and I wanted the surfaces as smooth as possible (no wood grain showing through)--that's why I thought masonite would be easier. Thank you so much for any advice.
~Lydia, in Idaho, USA

Welcome to the forum.
I suggest 5/8" ply which will span 3' with minimal sagging screwed to top edge of the 4" x 1" box, seal the face with a quality paint sealer, may need 2 coats sand each coat smooth before final coat.

Welcome Lydia

Thank you, Ray. I was trying to get away with something lighter (I have to lift these boxes up by myself and I'm not a strong person, but it makes sense to just build it right and then worry about what help I will need to have to hoist them up.

Welcome to the forum.