You have several possibilities for a picnic on a normal day (as Gayot Fow's answer mentions, the white picnic is worth the trip as well).
The first one is where everyone goes, particularly tourists - namely around the Grand Canal. I would not say that you need to "reserve" your spot but some places get crowded.
A picture I took in May, on a Sunday, from the left bank of the canal, where the Allée des Matelots meets the Grand Canal (showing the "crowded areas" above):
There is another place, where locals tend to picnic (more than tourists); This is also a typical place for children birthdays, starting from May
I would not recommend any of the boulangeries - they are great for bread but will be horribly overpriced for a picnic. Better bring in stuff yourself, there are supermarkets nearby (the closest will probably be Leader Price or Super U which is not that far either). There are others too but I know that side of the gardens better :)
You can now drive into the Versailles Gardens ($$), which can be practical if you need to carry a picnic for 27 people.
UPDATE as promised
You have a few places where you need to pay in the Versailles castle:
- the castle itself (with long waiting lines)
- the gardens right in front of the castle (on the other side). You can access them either from the side of the castle, or from the other side (there are two ticket booths on the path from the Grand Canal to the gardens). BTW access if free during winter times.
- the Hameau de la Reine, a little village built for Marie-Antoinette, worth the walk.
- the Trianons (small castles)
You probably can bundle some of these, I do not know because when I was actually visiting Versailles all of this was free and now I walk or ride on the free part :)
A rough map of the pay vs free areas (I missed the Trianon in the pay area). The line in blue are the roads where you can drive.
If you had to make a hard choice I would go for the Hameau de la Reine which is unusual. Still, the castle is nice, the gardens are nice too. It really depends on the time you have.
You can also rent bikes at the entrances of the garden.
There are light and sound concerts in the evenings during spring, summmer and automn - I do not know if they are nice, at least the sound and the fireworks are OK (seen from the outside)
All in all Versailles is a fantastic city.