What to put on top of existing vinyl
Self-adhesive tiles bond well if the surface is prepared well. If you can strip it chemically and apply a bonding primer you shouldn't have problems. 

To install vinyl sheet over vinyl you should usually level the existing embossing using, get this, an embossing leveler. You simply trowel it onto/into the texture of the old floor to make it flat. This technique does depend on both the old and new flooring products being appropriate for that use. 

What I'd do depends on how long I expect to be there. Chances are I'd find some nice rugs that I could take with me when I go.