Saga Edition is great in that the core rulebook really is all you need to run the game; everything else is just gravy.
That said, my recommendations on the other books would be as follows:
Starships of the Galaxy - If you are doing anything involving space combat, this book is almost mandatory. It gives you a much wider range of ships than the corebook does, as well as ways to use those big honkin' capital ships without too great a risk of inadvertently blowing your PCs' smaller ships into bits. The fun crunch that is the Tech Specialist feat and the Outlaw Tech talent tree can be found for free on WotC's Star Wars homepage (check the archives for web enhancements, it's the 1st or 2nd one for the corebook)
Campaign Setting Guide - If you are planning on doing a campaign within a certain setting (Knights of the Old Republic, Dark Times, Clone Wars, Legacy Era, etc), I strongly suggest picking up the relevant campaign guide (with Rebellion Era due in little over a month) as they all provide a great background resource on the setting they cover, with the KOTOR book being my favorite of the bunch and the Legacy Era a close second. Also, The Force Unleashed guide (aka Dark Times sourcebook) has a lot of great information on the Empire just prior to the timeframe of the Rebellion.
Scum & Villainy - Don't get me wrong, this is a really cool book, especially if you're running a fringe/outlaw campaign (ala Firefly/Serenity), but the Upgrade rules can open a very serious can of worms. This is a book that can wait a while before you pick it up.
Jedi Academy Training Manual - There's some great advice for how to best play a Jedi and avoid "lightsaber syndrome," but unless you're doing an all-Jedi campaign, this can definitely wait until later, as most of the crunch is a bit esoteric.
Threats of the Galaxy - hate to say it, but this one is largely a pass. The only thing that it really provides is a lot of NPCs, and you can find NPC builds for free all over the net, particularly on the Holonet Forums and WotC's message boards. Heck, click the link in my sig and download the Big Frakin' List of NPCs I compiled (over a 150 of them as of v1.2) if you really need a lot of pre-made NPCs in one easy reference.