Assuming the old floor is in good shape, you can put the new tiles
right on top. Just clean up the old floor so the adhesive will stick,
and fix any bumps or lumps in the old floor.
As for overkill, if you were going to level the floor etc, you might as
well take out the old floor - which could be a pain.......
Regular old self stick tiles should work fine and last a long time;
I think leveling the floor is probably overkill for this job