Versailles overwhelms on purpose, that was the point of building it. The move is to give the State Apartments their hour, then spend the day where it breathes: the fountained gardens, the Trianon palaces, Marie-Antoinette’s make-believe hamlet, and a rowboat on the Grand Canal.
Arrive for opening or after 2pm, when the tour-bus wave recedes, and book the timed palace ticket. On fountain-show days the gardens are ticketed too; check before you go.
The RER C runs from central Paris to Versailles Château Rive Gauche, ten minutes’ walk from the gates. Renting a bike inside the park is the difference between seeing the gardens and actually reaching them.