Filling the grooves with compound or caulk will not work well; either one will shrink and the compound may not stick well. The easiest way to get a smooth look is to cover the paneling with wallpaper liner horizontally. It is made especially to cover problem walls. Size the paneling with sizing concentrate mixed with water and use the recommended paste. Let that dry thoroughly before priming. For living room and bedrooms, use a latex primer like Zinsser’s Bulls Eye 1-2-3 and then a latex flat paint. For kitchen and other wet rooms, use their Cover Stain (oil) primer and an oil enamel.
There is more on painting on my website at http://www.bobf.info.