To get a proper paint job, that will last. Clean the cabinets, and make sure all grease, hand oils, cooking oils, etc is completely off the surface. Then sand them very well. Then wipe them all down and make sure, they are in a no dust environment. Prime them with a sealing bonding primer. Please check time to wait for painting. Then use a cabinet paint that is meant for cabinets, not regular house type paint. It will take 2-3 coats. Drying between coats time is on the can. Once you have them finished, wait a few days, before you put the hardware on, and the doors back on. Then be super careful for at least 30 days or so, for the paint to fully cure. It will dry to a hard finish, that will hold up longer. I do see the evidence in your picture, that someone wears a ring, while opening those doors. There isnt much of anything that will prevent that from happening, unless rings are removed in the kitchen, and I know that isnt likely to happen.

Agreed. Good observations and points.