I'll skip any comments on Robotech videos except to say that you'll get different parallel universes if you don't remember that Robotech is a meta-construct of other giant robot shows, one of which is Macross. I've seen a promo video of Robotech Shadow Chronicles, but not seen the whole thing so my knowledge is based on flipping through my book.
Having said that, do you want to mix Macross II mechs and gear with Robotech? You don't need the books if they remain separate.
I have the Shadow Chronicles book, for nostalgia, not because I've played Robotech anytime recently.
If you want to play during the invid invasion of Earth, then having the original book, Southern Cross book and of course the invid invasion are all good ideas.
You can probably get away without buying the REF Field Guide, but it was sorta nice having extra goodies. I think it was mostly reprinted/collected material from previous books.
The Shadow Chronicles occur after all the Robotech books, with the possible exception of the Sentinels, because the fleet that returns to Earth in the Shadow Chronicles is seen in the final episodes of the invid series.
I read the Del Rey novels about the expedition to find the Master's homeworld and so my memories of the cartoon have blurry edges where they meet the novels.
Lancer's Rockers is ridiculous crap, unless you want to fight mutant Commie-Invid mecha. The EBSIS is the Robotech universe version of the USSR.
Robotech New World Order you can probably do without, unless you want pre-written material on Africa and other places after robotechnology and giant aliens invade.
RDF Accelerated Training Guide sounds a little like what it does. Essentially training missions for new recruits, i.e. your players. It is pre-made adventures, all combat related, but then again, this is Robotech we are talking about.
Ghost Ship is another book of missions. If your players want to repeat the actions I remember happening from the cartoon, i.e. a few fighters taking down battleships, this adventure could be for you. I think a crippled Zent ship is detected or is playing dead to trap the good guys. I think it has a random techno-control chart for what the Zent's call things like batteries or a light switch.
If you want to create your own Robotech universe, then you can maybe find a good mix of Robotech and Macross II stuff. The problem is power creep. The Macross II stuff can absorb more damage than anything in the Robotech universe. The idea I originally had was that after the invid leave Earth, the Marduk show up, (with enough time for humanity to recover). That's why the mechs are similar yet different and better, and why you have Zent's still around, because the hormones wore off and they can reproduce with each other and humans. The Marduk want to wipe out their former underlings, the Zents, and humans. Or conquer them, whatever. How you accomplish this with the Shadow Chronicles books may have a bit more rough edges to sand down.
I have to admit that the mechs for Macross are pretty dang cool. I love the drones and the transformable Marduk battle pods.
Another option I realized. Drop Earth completely. The humans can be from another planet and you can insert your own background, just use the stats.
I might have more info about the other books, but I should be doing reading for class right now.
