The following is where you all will be able to find information in the rule books that will be most useful to you in this campaign. The only reading that probably ought to be required is at least skimming the stuff I'll point out in the core book. Almost everything else, I will try to at least briefly summarize on Obsidian Portal.
Exalted Second Edition Core:
Chapter 3: Traits
Chapter 4: Drama and Systems
Chapter 5: Charms, Combos and Sorcery (ignore the combo rules for now, we will be using a houseruled version of them) (Just skim this chapter for now, it will likely overwhelm most of you right now)
Chapter 8: Panoply (Just skim this section and get a better idea of some of the equipment that is available to base characters; much of what you'll be using will be modified versions of this stuff)
Manual of Exalted Power: Alchemicals
Chapter Two: Subgods of Autochthonia (Skim this for a rough understanding of the world of Autochthonia, but don't worry about it too much)
Chapter Six: Wonders of the Machine God (All of this equipment will be standard, normal, everyday stuff to your characters)
Shards of the Exalted Dream:
Chapter One: Gunstar Autocthonia (Skim for a better understanding of the game setting we are using. Expect some things to not make sense yet.)
Scroll of Errata:
Anything related to Solars or the core system
I am not saying you guys need to read all of the above, or all of the books on the share drive.
I am saying, however, that anyone who takes the time to browse through the chapters I've suggested above will have an advantage in being ready to make a character and start playing.
Let me know if you guys have any questions.