The Passport covers a full day of Palace and Trianon visits, including the Gardens. Today's standard rate is €25, or €22 for EEA residents or nationals.
Your Palace entry needs a booked time slot. You can visit the Gardens and Trianon during their opening hours. The Passport includes daytime garden shows when they run.
From Paris, RER C serves Versailles Château Rive Gauche, a 10-minute walk from the Palace. The transport guide has routes and walking times for the other Versailles stations.
For the Palace to Trianon leg, the little train takes 20 minutes. A circuit costs €9 at the full rate. Electric vehicle hire costs €42 per hour.
For a picnic, use the Park. At the Petit Trianon, Angelina has a terrace and food stand. The Palace's facilities page gives the location of the food stop.