It depends on if you will apply a texture to the ceiling or go for a smooth look. Basically, the more or heavier the texture the less you need to do. I will explain what it will take for a smooth look.
You need to sand to remove any remaining residue from the acoustic texture. If there are any water spots or stains these will need sealing. Now you have to check all of the drywall seams, joints and nail/screw heads. All of these areas need to be flat and level with the ceiling. Apply drywall mud were needed.
Also any damage or deep scratches to the ceiling from the removal of the texture will need fixing. Any damage or unevenness will become more apparent when the ceiling is painted.
After all repairs are finished and sanded smooth the ceiling will need priming. At this point you will easily see any faults in the surface, fix were needed. Before painting I recommend caulking the joint/angle between the ceiling and walls.
Now you are ready for painting. If some type of texture will be applied then the surface doesn't need to be as perfect as a smooth ceiling.