A few months ago, I helped my friend at the body shop re-do a 68 coupe with a vinyl top. The top was original and pretty much shot. Just grab an end and start pulling. As Conejo172 said, there were a few areas we had to use a box cutter on to get it started. The trim has to come off. Once all the vinyl is gone, you're left with a bunch of dried glue. A "DA" sander and some 80 grit discs should take care of it. We took it down to bare metal. Shoot a coat of epoxy to preserve your work. Then you can make your mind up if you want to re-do the vinyl top or paint it. If you're going to paint it, you have to fill the trim holes.
The customer decided to add a new vinyl top. The shop that was doing the work requested that the top be painted. Not sure why but we shot a coat on anyway. That's my experience. Hope this helps.