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oldfag here. Been watching anime for about 30 years and I've seen the best of the best. I will give you my personal list of the best anime.
Armored Trooper Votoms (My mecha recommendation)
Ashita no Joe (greatest sports anime ever made) (There are 2 series separated by a decade but it's important to watch both)
Berserk 1997 (common but must be said)
Black Jack (OVAs)
Black Lagoon
Casshern Sins
Cyborg 009 (both the 1979 and 2001 series)
Chobits (one of the few comedy romance anime I found to be fun and enjoyable)
City Hunter (second series is better than the first but all of it is incredible and is one of the greatest shows of that decade)
Dororo (one of the few recent shows I found to be good)
Genshiken
Legend of the Galactic Heroes
Golden Boy (OVAs)
Golgo 13 (fun stuff)
Great Teacher Onizuka
Requiem From the Darkness (not one of the best shows but boy is it great to look at)
Lupin III (all of it)
Michiko to Hatchin (ending is shit though)
Monster (one of the best ever)
Shiki (if you want some spook)
Space Adventure Cobra
Takarajima
Trigun (common but needs to be said)
Captain Harlock (If you want some Leiji)
Rose of Versailles
Welcome to the NHK
I don't fuck around. If you really want suggestions, always aim high and never take a bad rec which unfortunately can be found in this thread. I tried to not name off mostly normie shit because we've all heard it a billion times. I wanted to give you some shit I know you haven't seen while also being the best of the best.