We just moved to a new home, one of the room has white wallpaper, without textures, which was painted with water based painting, so it was easy to repaint. The other rooms also have white wallpapers but the painting is not water based. It looks as oil based paint. Is it a good idea to repaint these wallpapers? If yes, what kind of paint do we need to use - (oil based paint and paint thinner)? Is it a good idea to remove the wallpapers and use water based paint?
In my personal opinion, it is always worth it to remove wall paper. Even if this one doesn't have a strange texture to it, it's always easier to patch holes or similar things later if you don't have an extra layer of vinyl to deal with.
Wall paper and glue can really vary-- some of it is a royal pain to remove, while others just peel right off the wall. I've had both in the same house. A spray bottle of warm water really helps. You might need to poke holes in the paper to let the water through; this tool makes it really easy to do so by just rolling it around on the wall.
In my opinion, your painting will definitely go easier with less hassles if you aren't trying to paint over vinyl. Of course, "the proof is in the pudding": if painting over the vinyl works for you, there is no overwhelming need to remove the wallpaper. It really is a personal preference; whatever works for you will be good enough.