You can use a satin or semi-gloss, actually sheen will be a personal preference. I would use a semi-gloss for the look and ease of cleaning. A hard finish would be best, so use a trim enamel paint.
Both a brush and roller will be used. The roller cover will need to be a tight short nap, 1/4 inch or mohair. The brush is used to get the groves and cut-in the top and bottom (places the roller can't get). Work in sections and work quickly for a nice even finish with the roller. For added comfort and a smoother finish condition your paint, use Flotrol or equivalent for latex paints.