To be honest, the best thing is to start at the beginning with the "Decision at Thunder Rift" paperback novel. It is the beginning of the Grey Death Legion series. I would leave the Clan books alone for now. If you can find them online, or maybe in PDF format all the better. The game is set before the invasion of the clans, or I should say before the clans are even known as more then just a new Pirate Threat on the Periphery, unless you are part of the Explorer Corp in ComStar. (And even the Pirate Threat is more rumor then fact for the IS.)
Also, something that you might enjoy if you can find them, are the Tech Readouts from 3050 and before. It will give you a better idea of the tech. Another resource that you could look into, would be the Readout books for other things as well. There are manuals for the differing Great Houses that will also cover things like what Mechs are prevalent, and there are Manuals for the Merc units to give you a better idea of the groups and how things are covered in Battletech.
To be honest, there is a complete flood of materials out there. You are looking at a game that has been a part of history for the last couple decades plus. It has become more and more polished through the years, and many of us on the forums have been "fanboi's" since way before the term even existed.
Edited by Papertarget, 03 July 2012 - 11:18 AM.