How thin is the thinnist you would go and the thickest you would go with wafer board or plywood.  It is going on the inside of the barn but on the outside of the house inside of barn which will be alleyway wall and also on my tackroom/office across the alleyway.  thanks  Or the cheapest wall covering

I want to say we use 1/2” for about everything.  It’s substantial enough to take a little bit of a beating and to hold screws to hang things up (although you’ll still want to go into a stud for heavier items like saddle racks, I’m talking like bridles, pitchforks etc).  

Use 1/2 to 3/4 PLYWOOD and not the glued together wafer board since in time it will disintegrate or your horse may like the taste of the glue and turn into a termite ..  

If you want the tuffest stall walls that last forever .. check with local sawmills for rough sawn oak boards 1x6 or 1x8 ... they must be installed while green sawn due to how tuff they get when dry. 

Use deck screws instead of nails on the oak .. no chewing or sucking on the oak and most durable and it is sold by the board ft ...