Silicone or plumbers putty?
Neither. The rubber gasket replaces both. Plumber's putty is mostly obsolete these days (almost everything comes with rubber or neoprene washers) and can stain fixtures, and silicone is never a good material for joining water-bearing plumbing components. 

You could use PTFE tape as a secondary measure and a thread lubricant. Be sure to wrap it the correct direction.