What is the best paint to cover vinyl wallcovering?

http://www2.benjaminmoore.com/en-ca/for-your-home/painting-over-wallpaper

If you use liquid sandpaper to dull the finish, prime and then paint over with latex paint.

I would discourage you from doing this. Vinyl wallpaper is meant to be water resistent, or sometimes even water proof. It is not meant to be a surface for paint to adhere to. The paint will likely not cover evenly, and will change the texture of your walls. If the result does not meet with your expectations, or if you ever change your mind, the whole shebang will be an extremely hard mess to try to remove!

Painting over wall paper is not a recommended practice,down the road it will bubble and peel making the wall very difficult to repair

Please, take the time to do it correctly and remove the wallpaper. As the glue loosens from age the wallpaper will have to be removed and all your work will be for nought. Plus you will be able to see the wallpaper under your paint.

Are you talking about the vinyl covered wall board? The kind found in mobile homes & RVs. If so, I painted over lots of this several years ago.

I started by washing the walls well with TSP. Then I used a good primer. One that they suggest you use to cover oil based paint with latex. I used latex throughout, in the kitchen & bathrooms I used latex made for these areas.

As this was about 20 yrs ago, I'm not sure, but I believe I did a couple of coats of primer as I was covering up a pattern on the vinyl.

The paint held up very well and had many many scrubbings. We continued to live in this home for another 7-8 yrs. The paint in the kitchen & bath still looked like new even with all the water from showers and the splatters in the kitchen around the sink and stove. I can honestly say it almost looked as good when we sold the home as the day I finished painting!