I haven't watched seasonal stuff in a few years, so you won't be getting any of those.
Classic and/or essential /a/core:
-Cowboy Bebop (Popular for a reason)
-Madoka (Watch the fancut, which combines the recap movies with the other versions.)
-Madoka Rebellion (The ending to the story, not to be missed.)
-Neon Genesis Evangelion (Inspired many other anime/memes/etc.)
-Code Geass (Inspired many other anime/memes/etc.)
Classic manga you should read instead of the anime:
-Akira (The movie only adapts the first 3 volumes out of 6, and cobbles together its own original ending)
-Nausicaa of the Valley of the Wind (The movie only adapts the first 3 volumes out of 6, and cuts out basically all characters except the protagonist)
Other magical girl shows:
-Nanoha Season 1 (A bit dated, but sets up future seasons - you can watch the movie which is very pretty, but only after watching the broadcast version. Or, you can read a transcript of the sound stages, which the movie adapted the most important parts of)
-Nanoha A's (The peak of magical girl shows - the movie is pretty but not a good adaptation. Make sure to read the companion manga.)
-Nanoha Strikers (Goes full in on the military aspects alluded to in earlier seasons, very slow in the first half but there is a payoff. Make sure to read the companion manga.)
-Mai-Hime (A magical girl show, ecchi comedy, and serious romantic drama fight to the death for dominance until the magical girl show wins.)
-Symphogear Season 1 (A little weird, they don't really know what they're doing yet.)
-Symphogear G (The peak of magical girl shows.)
-Symphogear GX, AXZ, XV (only if you can't get enough Symphogear, as the other 3 seasons are notably worse in quality)
-For all Symphogear seasons, make sure to read transcriptions of the song lyrics for extra lore.
Other Anime
Iria Zeriam
Outlaw Star
Excaflowne
Eureka Seven
Psycho-Pass S1
Ghost Stories (Dub)
Redline
Manga
Spirit Circle
Dungeon Meshi
Azumanga Daioh
Berserk
