We're trying to decide whether to leave down the old vinyl flooring tile in the house we recently bought. This article makes some good points about the advantages of vinyl.
We probably would have removed the vinyl immediately, but then we learned that we would need a special machine to remove it. I am told that most people simple place vinyl floor coverings on top of one another instead of removing the old flooring.
I would rather take up the old and start fresh, but this sounds like a tough job, especially since the old vinyl has a couple uneven spots that need to be taken care of somehow before putting more flooring on top.