We built this house 15 years ago so I'm sure their isn't asbestos in the floor, and I know it's plywood underneath. We're a huge believer in doing a job right the first time, so we'll rip up the vinyl. I hadn't thought of laying the CBU over the vinyl...
That would definitely save a lot of time and mess.
We're picking out carpet for the adjoining rooms tonight, so we'll be able to make a final decision about the tile soon.