I use Windex. For buildup that's too tough for Windex I use Bon Ami, a non-chlorinated abrasive cleaner, or my glass polishing compound. Once clean, I treat the windshield with a RainX-type of compound.
Are you sure the windshield isn't etched? Sometimes, you can clean the windshield and put new wiper blades, but on a wet night you'll still see a stain pattern that will not go away. For this you'll need to use glass polishing compound.