Painting laminated cabinets and doors requires critical preparation, cleaning, sanding and priming. We like TSP or a degreaser and it must be thoroughly rinsed from the surfaces so the primer will adhere.
Then the surfaces should be roughed using an abrasive kitchen scrub sponge or sandpaper. Do the boxes, doors, moldings and sides until the sheens are scuffed or gone. Again, clean the surfaces of the dust and use a tack cloth.
The primer I suggest is BIN. It is alcohol based, dries in 30 minutes and has tremendous bonding. I suggest you tint the primer to help paint coverage.
I use 100% acrylic latex paint for the finish coat. It is very hard and resistant to hard use. Try to find paint designed for trim, usually called enamel. Some of these hardy paints are mixed specifically for cabinetry and are as resistant to scratches and abuse as oil based.