It's generally regarded that skimming gives a better finish, especially for a kitchen ceiling, but you don't have to do that.
As long as the boards have been taped and filled well enough to hide the joins, you can paint directly onto them. Either use a specific plasterboard/drywall sealer first or a mist coat of matt emulsion (around 20-25% water) to seal the boards before applying your finish coat(s).
As for paint, acrylic eggshell is best, closely followed by a specific kitchen paint.
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