I would use this self leveller, the magic of gravity will do a much better job than the human eye.
There is a acrylic primer to use before hand.
After that you can put your flooring right over it, so it says on the package. It is cement and some polymers.
Floors are deceptively difficult to level, shimming it would be difficult not to mention creaky. Cardboard will depress/degrade and therefore useless, if you want to do that you can use roofing felt.