I am more familiar with race type trailers, but the construction is similar. The best walls I have seen on those is 3/8" plywood, I would use the good-one-side variety to make a nice smooth base for your finish layer. Anything I have seen thinner than that ends up flimsy even on 16" centers. 1/2" is overkill and just wastes weight. I have built heavy duty shelving in all of my trailers over the years, screwed to the 3/8", and it is plenty strong. I can't imagine a need for mdf behind that, once again it just adds weight. Insulate the walls to keep it quiet.
Then you can use the thin paneling or wallboard over that. I have seen good jobs with panelling, or white board, or the pre-covered sheets that dragonslayer mentioned. Stagger the seams from the plywood to the paneling so you don't have to staple the battens over the plywood seams, you'll get a better result.
I was in Elkhart recently, and Johnson's surplus had the whiteboard for the ceiling for $8 a sheet, and Bontrager's had the wall board for about $10 a sheet. Batten strips were a buck.
Screw the plywood to the wall studs with the flat countersunk screws. Glue on the wall board and use a staple gun for the battens. Done.
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