Foro:
Annihilator's classic album certainly is
Alice In Hell. It's basically a 37-minute mother of a riff-fest, and one of the (if not THE) greatest thrash metal albums ever. Never, Neverland is, as I said, a brilliant album too. How can you not like an album that has a song about macaroni and cheese?
After that, King Of The Kill is another must-have, but other than that, it's always a bit of a hit-and-miss with them. Waters is basically a miniature Schaffer, and in contrary to Iced Earth, Annihilator really suffered from all those lineup changes they've had.
Invader:
In addition to those you mentioned, I would heartily recommend Anthrax (one of the "Big Four" along with Metallica, Megadeth and Slayer), Sodom, Exodus, Overkill, Flotsam And Jetsam, Holy Moses, Possessed and, above all, Exciter (they are not as "thrashy" as the others, but they pretty much founded the genre). Once you're somehow acquainted with those, you should have a good basic thrash gear. At least get
Among The Living (Anthrax),
Bonded By Blood (Exodus) and
Heavy Metal Maniac (Exciter) as soon as you can- they're essentials, no matter what their availability says (in fact, the Exciter album is impossible to find in stores, so I guess downloading it isn't a sin). Oh, and if you've licked Bay Area blood, go for Heathen (you can legally download their albums on their website for free) and Death Angel next. Finally, perhaps Destruction should be mentioned as the third big German thrash band (after Kreator and Sodom), but I personally have no use for them.