Removing old paint so yo t

You don't have to remove all paint to repaint. If the surface is glossy or in the least bit shiny just scuff with sand paper to give the new paint something to grip better. Also make sure cabinets are grease free (hand prints, kitchen grease) or the paint will not stick.

Sanding.

Em is correct. After sanding, prime with oil based primer, put two coats of oil based paint on.

Take one of the cabinet doors to the paint department of the home improvement store and ask them to select paint/stains and other finishes and application tools that will work for your kitchen. They have the best selection, the most up-to-date materials and most important, the most informative sales staff to get you what you need for a professional job.