Well, Annihilator - or perhaps I should say Jeff Waters, since he IS Annihilator - are an extremely frustrating band. With the talent he has on guitar, you'd have expected more quality throughout the significant number of albums they put out. Alas, for the most part, that's not the case.
Alice in Hell is the other generally recognized "classic" in the discography. I think it's great (although not as good as Never, Neverland), but I get that you might be put off by the singer.
Their third album, Set the World on Fire, is an interesting one. I personally love it, but don't expect anything similar to Never, Neverland. The thrash is mostly gone and the sound is overall much softer. Yet, the songs are great, in my opinion, and the guitar work is excellent. And it has Mr. Mangini on drums (for most, not all, tracks)! Lyrics are mostly on the silly side, as you'd expect from the band, but it doesn't matter that much. Check out the title-track, No Zone, Knight Jumps Queen and Brain Dance (the latter is all over the place) for heavier stuff, Bats in the Belfry and Snake in the Grass for Annihilator's unique take on hard rock/classic metal. There are a couple of ballads - Phoenix Rising has more of an epic feel, somewhat cheesy but effective, Sounds Good to Me is a bit unusual and musically interesting - it's pretty up-tempo and it has these beautiful, clean arpeggiated guitars all over (Jeff Waters is a master of those!). Anyway, give it a try. The quality is there, you just kinda have to forget it's Annihilator
After this, um, it's a bit of a mess. The following album, King of the Kill, has Jeff Waters himself on vocals. He's not terrible, actually. There's some reprise of a slightly thrashier sound, but the album is again pretty varied. Some decent songs (the title track, Hell is a War, Second to None), but it was a disappointment for me when it came out. Plus, this is where Waters starts the tradition of rehashing large chunks of old songs, literally. Previous albums would have some nuggets/throwbacks, but it gets worse from here.
After a couple of missteps (Refresh the Demon, Remains) there's an attempt to go back to the fast 'n' heavy roots with Criteria For a Black Widow. I never particularly loved it - plus, it has the singer from Alice in Hell, so it might not be for you
Then comes what I personally find the last
all-around good Annihilator album: Carnival Diablos. Another change at the mic, this time bringing in Joe Comeau, formerly in Overkill (on guitars, though). He does a very good job, and has an uncanny ability to mimic a variety of vocal styles (from aggressive, to Halford-like, to Dickinson-like). Which, incidentally, is also one problem with this album: generally very good songs, but it almost feels like it was written as a compilation of songs in the styles of different bands - Judas Priest (Time Bomb), Slayer (Hunter Killer), Iron Maiden (Epic of War), and AC/DC (Shallow Grave) - so it sounds kind of gimmicky at times. But the riffs are great again (Denied, Battered), the title-track is very cool (with a beautiful Rush-like melodic interlude) and there is an instrumental (Liquid Oval) where Jeff Waters once again showcases his melodic sensibilities. This is overall a fun album, and I'd recommend a listen.
There's a second album with Comeau, Waking the Fury. Not bad, but a drop in quality for me (plus, the guitar sound is bizarre)
Then you have the Dave Padden-fronted era. He's actually a pretty talented dude, also playing guitar live. The voice is a bit of an acquired taste, I guess. But he was the singer with the longest tenure in the band (5 albums). This overall becomes a blur for me, as I stopped following closely. What I heard was very inconsistent - both across and within albums. Maybe someone here with better knowledge of this era can point you to the better material. I can tell you that, among the ones I've heard, I found "Feast" (2013) to be pretty good. It's also the last with Padden.
After that, there's three more with Jeff Waters back on vocals. I think I've listened to them a few times here and there, and the general impression was a newfound aggression, but also way less creative riffing and LOTS of recycling
Sooo...LONG story short...if you are wondering where to next - I'd say try Set the World on Fire and Carnival Diablos. Both different from what you've heard, but still good. Then maybe Feast, and a couple of the recent ones (the last is 2020) for some more aggressive material with Jeff Waters singing. Let me know how this goes!