Wood filler(Elmer's Fill n Finish) works just fine. Like TRN said, the regular Elmer's filler will work too. Thin with water to a pancake batter consistency. Brush on, and into the spiral grooves. Sand smooth with 320 or 400 grit.
Several coats of grey primer will work too, but seems like way more sanding involved, and messier IMO. One coat filler and one coat primer is generally all I need before applying a top coat.