Yup, it's better to strip the wax first before polishing.
But before you go ahead with that, you may wish to consider professional polishing to get rid of the swirls so you have a good base to work the wax on.
If however, you decide to go ahead and DIY, you can strip most of the wax with a diluted concentration of dishwashing liquid and water. The surface should feel squeaky after that.
If I remember correctly, Gold class wax has no polishing properties. You cannot get rid of the swirls this way. keke. I pressume the level of swirls is not deep - i.e. only visible under certain angles and/or under strong lights. Try some of the milder polishes out there. #7 should be quite suitable if you're going the machine route.
Pingman's recommending #20 (Polymer Sealant) if I'm not mistaken. This should come after you finish polishing.
Cheers,
Alvin.