Which books should I start out with if I want to read about the TOR era?
Have you watched the timeline vids?
Fatal Alliance, Deceived, and Reven releases on the 15th of this month. Deceived is a must read imo. It gives a lot of backstory on Malgus. Those all tie in with the TOR games.
For books, go with Fatal Alliance, Deceived and Revan as they really help set up the game. If you haven't already, I'd also go play Star Wars: Knights of the Old Republic and Knights of the Old Republic II: The Sith Lords.
Does it matter which order I read them in?
Try this and see if that doesn't help you out. I actually need to get to reading if I'm gonna manage to pack that list in by launch.
Don't forget the Timeline videos : http://www.swtor.com/info/holonet/timeline