Back in the day, for me it was Slayer, Anthrax, Megadeth from the big 4. Weirdly enough, I didn't get into Metallica until later. I had this impression that they were not as "punk rock" as the other 3 and I thought the name sounded like a faggy hair metal band that wore high heels and shit.
As far as other thrash bands went, I loved Forbidden, Death Angel, Testament, Sodom, Kreator, Destruction, Flotsam & Jetsam and Vio-lence. I didn't really listen to Exodus at the time, and I didn't like earlier Overkill. Also worth a mention is Forced Entry from Seattle. As Above, So Below has some pretty impressive material on it. My drummer at the time was really into Prong. I didn't really get into Prong until the Cleansing album.
If I had to pick favorites, I'd go with Forbidden and Death Angel, and maybe Kreator.