First time coming across your reaction, sorry about your grandpa. I'm a big Anthrax fan, and you pointed out the drums. Charlie Benante, Anthrax's drummer, writes all their music. Then the band meets, or he'll send them what he's written, and they'll tweak what he wrote, but almost all of it is written by the drummer. He's been with them long enough, working with the band, he knows what each member likes to play, and incorporates it. As a big fan of Anthrax, both Joey and John eras, I think for shredding, you might like Skeleton In The Closest, but check out the Live In Chile version. It has the Shadows Fall lead guitarist in Anthrax, and think it really captures how intense Anthrax can be, while still being Anthrax and having fun. My favorite solo in any Anthrax song is Safe Home, with Rob Caggiano playing lead guitar. The studio version of Inside Out has Dimebag Darrel playing the solo. After Dan Spitz left Anthrax, they didn't have a lead guitarist officially in the band. They toured with Paul Crook, but Dimebag would play on a couple songs from each album until his death. Charlie would write the songs, and send them to Dimebag to choose which songs he wanted to play on.
oh, crap ...I just remembered you said it was ok to make requests in the comments... I know it's been done to death, but I hardly ever see any actual guitarists react to it--- would you consider checking out Eddie Van Halen's live solo...I think it's called "eruption live solo" or something like that? ...even if you've already seen it I'd love to hear your thoughts on it.
Among the big 4, Anthrax and Slayer did not have good solos, but Megadeth & Metallica were awesome of course. You should check out the Thrash band Warfect and their song 'Pestilence'.
