Which background books are the best purchases for the Spinward Marches?



I'm new to Traveller, having played D&D on and off for the last 35 years or so, and I'm just wondering which books to buy for general Spinward Marches background info. I'm thinking that we'll be starting with Marches Adventure 1 - High and Dry and then perhaps work through the rest of the Marches series, sprinkling in a few other adventures along the way.

I have ordered The Third Imperium and Behind the Claw, is it also worth getting the Spinward Marches 1 : The Bowman Arm eBook or will the contents of this be covered in the other two books?

Also, is there a book which is an introduction/overview of the official universe? Or is that book actually The Third Imperium? I'm thinking of something like a background equivalent of the Explorer's Edition, as that would be really useful as a kicking off point. For each area (sorry sector/subsector ;-)) it could then refer the reader to other books which provide more in depth coverage of that location. Oh, and how cool would it be if it also listed the official adventures/campaigns/expansions that take place in each area as well, pulling the whole thing together. This would be just the thing for newbies like me where it all seems impenetrable at the start. Perhaps would be good as a pdf so that it could be updated easily, however, I would be happy to buy a printed version as well.