Plaster stuff is falling off the ceiling

When we got our house we could see that there was some water damage around our skylight that had been repaired. Slowly over time the bubbly repainted edges started crack and fall and soon all the plaster (the non-repaired) part started falling off with it. It looks horrible and I got an estimate which was going to be $2000 to repair with replacing the skylight. I ended up getting a new skylight and replacing the 7 year old roof because the previous owners did it themselves and did a horrible job. My insurance wouldn't cover the roof because it was installed bad and the inspector should have caught it. So I'm going to fix the ceiling myself. I have no idea how to plaster or anything. I decided to put beadboard wall paper up there.

So my question is this. Do I need to go ahead and try to knock down all the plaster on the ceiling or just the loose and cracking areas? And can I apply it directly to the gray rough part of the ceiling (no clue what its called). TIA!