There are a couple things I found that should be kept in mind when using PVC. First, it is softer than many other materials and you can dig into it very easily. Keep sharp tools and use them in bevel rubbing mode rather than scraping. Use a light touch and even strokes.
Stop the lathe often to remove the ribbons of plastic.
I like to use a skew to smooth it as my final cut.
For finishing I sanded from 220 to about 600 (actually MM2400) then I buffed. When sanding, use relatively slow speed and a light touch and keep it moving. I wet sanded using water.
I don't have the fancy Beall buffing system. Mine is a Harbor freight special. It is a 4" loose wheel on an arbor that has a 1/4" shaft. I put the wheel in my collet chuck and buff on the lathe. Keep the pen at a 45 deg. angle to the rotation of the wheel. I use the blue "plastic" buffing compound also from HF. Use a light touch and keep it moving.
I like the PVC, but it actually takes me longer than wood. But I readily admit I am not great with plastic materials of any kind.