^this.
Machine polishing vinyl is not a good idea. Way too easy to damage it and scratches and swirls in vinyl don't polish out.
Revive Hand Polish is a great product for vinyl, as it is more of a cleaner than a typical polish, since it does not contain any abrasives.
If you need to polish the paint next to the vinyl, tape off the edges of the vinyl to protect them from damage by the machine, and to keep product from building up on the edges.
While some people will apply a wax or sealant to vinyl with a machine on low speed, I find that it just gets too much product on the edges. Best to do these areas by hand, too.
Once you get the vinyl cleaned up, use
Quick Sealant or
Super VRT to add some protection. If your vinyl is gloss, then you can also use a wax for protection (no wax on matte vinyl).
-Dan