Depending on how bad your existing floorboards are depends on which thickness of plywood to install.
In my experience, at least 6mm or 9mm thick plywood normally does the job. Ignore the hardboard as it's only 3mm thick and would just follow the contours of your existing uneven floorboards.
Never put anything soft or pliable under vinyl flooring as there's a good chance you will puncture or tear it when walking on it.
Any flooring is only as good as the prep work that is underneath it!