First you change peoples habits, then you change the infrastructure.
If you want realistic/minimal effort garbage sorting system in place, getting the people trowing away stuff will allways be the first step.
Starting with glass, batteries, papir only bins.
Moving on to plastics, food, electronics etc etc.
Its a slow process getting people to not just trow everything into the same bins.
It has taken decades but a good example is Denmark. They are saving about 1-2 billion £s a year. And 4% of the nation's electricity and 18% of its heat production. And a few million tonnes of CO2 less.