I agree that the MDF panel is a better product. More stable. If you are concerned about the grain, an MDF panel with a matching veneer is available. If you are using maple for the balance of the door construction, MDF is fine! As to the finish, lacquer is traditional for finish. Some finishers have issues with custom colors of lacquer, so other finishes are suggested. Lacquer is sensitive to water, more so than other finishes. Keeping it dry around the sink and not hanging wet towels on it is important. Oil based paints (unavailable to use here in NorCal) are the second option. They go on thicker and in the wrong hands, can obscure fine details. Same with other paints. Paint chemistry is changing fast. Toxins that made it strong and last long are coming out. Most manufacturers offer some kind of "green" low VOC paint. I used Aura satin on a wall of Wardrobe cabinets and it is a pretty good finish. Trust you finisher!

If you are looking for a smooth finish, the yes the MDF panel will be great. Here we use a lacquer finish and have not had issues.