If you want another skim coat, clean the current ceiling well. Then consider using a bonding agent for better adhesion between the new and old work.
Figure out what you want to skim coat with, then find a bonding agent that will work with that product.
Plaster is fairly easy to work, though with it being your first time don't expect a glass-smooth surface.
You can also tint the plaster which will give you a very nice effect.
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