Hello,
Last year I put up about 120 sheets of this stuff in my shop (36x50, walls, ceiling, and dividng wall).
I put it smooth side out, though I sort-of think it would have been better the other way. The ridges would never be as smooth as the smooth side but after it's painted it may look better since the chips on the smooth side show through even with primer and paint. I don't know for sure. It might be an interesting exercise to paint both sides of a scrap of it and see what you think before you hang any of it.
I primed mine with Zinnser Cover Stain oil based primer (not 1-2-3 which is water based, and not BIN which is a shellac). I managed about 250 sq. ft. per gallon, maybe 300. I put it on with an 18" wide roller cover and either a 1/2" or 5/8" nap (I don't remember). I've painted the ceiling that way, and have done some of the walls but not all of them. It's on the list, I'm just slow working by myself.
I used one coat of that, and followed it with a single coat of Behr eggshell white, Paint/Primer in one. I used that to try to avoid having to do multiple coats of paint, and I'm okay with how it has turned out so far.
I'm also running a bead of silicone between the bottom of the OSB and the floor as an additional barrier to moisture.