Some quick background to preempt some discussion about quality, longevity, rental issues, etc.: I'm in a rental that is literally "anything goes". It's a long story, but suffice it to say if it does not require a building permit (or does but you can hide from the inspector), it's good to go. This is an open layout where the bulk is laminate flooring that I installed myself. I have an area that's approximately 18' x 8' that's an entrance and kitchen area and a bathroom that's about 6' x 6' where the original floor is still exposed. The original floor is the old fashioned "linoleum" (asphalt/asbestos 12"x12" tiles) flooring. It's in OK shape, but looks horrible - there's no cleaning of it at this point - it will never be white again.
My main goal is to put the cheapest vinyl solution on top of this that I can. A lifespan of 5 years would be beyond what I'm aiming for. Tearing up the old floor is not an option, nor is any floor prep that involves sanding (I am not wanting to kick up asbestos). I assume I need some type of stripper, but I'm not finding any good specifics about that online.
My second goal is ease of installation. I can't see myself doing a good job with a large sheet - the kitchen/entryway is sort of an elongated "U" shape ( |__| ), and the bathroom is small, but I have to go around the toilet and a small vanity. And having an open floorplan like this, I'd like to avoid stinking the place up with the adhesives required for sheet flooring. So I'm aiming for the self-stick stuff.
Any recommendations on cheap stick-on that will stick, and probably even more importantly the materials to prep the existing floor are welcome!