There are so many options when painting cabinets. You can use oil, if you can find it , or melamine paint but I always use LATEX . I most often use satin finish but I have also used semi-gloss. Once the paint has had time to cure it is quite durable. The satin finish minimizes any flaws and the grain in the oak that I am painting.
Although I wish that I had a large compressor and an air spray gun I used an angle paint brush for the details on the doors and a foam roller.
I do not over load the roller , I use long strokes over and over until it is a nice smooth finish and make sure to correct any mistakes before leaving it alone. Don't mess too much while applying latex paint , it dries very quickly...
So that's really all there is to it , I use latex paint in satin and apply two to three coats by brush for the details and foam roller and allow to dry before re-attaching the hinges. I just finished the final coat and I will wait till Tuesday to re-install the door on the one side of the kitchen. I can't wait to see it all together .