Definetly pick up peace sells, so far so good so what, and rust in peace, maybe countdown and youthanasia too from megadeth. Mustaines voice isn't really screaming it's just that he sucks at singing at takes a bit to get used to
Basically the big ones for thrash that I'm away of are Metallica, Slayer, Megadeth, and like others have mentioned Testament and Anthrax. Maybe try Overkill and Exodus too.
Check out a genre called Power Metal too. It's basically very fast, melodic guitars with very melodic singing too which is what seperates it from thrash metal, also the lyrics and keys tend to be more uplifting than dark and depressing as in thrash metal. Currently my favorite band in this genre is an Italian band called Rhapsody if you want an example.