talk to your local health department for lab that does asbestos testing. Maybe you will get lucky. Old vinyl has to be scraped off with a sharp flooring scraping knife with a 3' handle. Home cheapo has them.
If it has asbestos and/or if it is stuck to 3/4" subfloor, then leave it cause you need to put 1/2" of cement backer board to create a solid surface for ceramic tile which needs at least 1 1/4" of floor under it. You will actually loose space with a ceramic tile floor so adjust accordingly along walls, cabinets, and door openings and use appropriate trim.