Plumbers putty is the wrong thing to use. Check the label of the container, it will tell you to not use it on anything plastic. Using plumbers putty will only work for a short time on plastic and then it will fail. Trust me, I have fixed ceilings under baths because of this common mistake.
The correct product is silicone in this particular situation. Contrary to the negative rep it gets here it does have its place and this is it.
There should be nothing but silicone between the basket and the top of the sink. The rubber and paper gaskets go under the sink.
