Gunbuster

As the daughter of a legendary space captain, Noriko Takaya sounds like she should have an edge at her military pilot academy, except she's kind of terrible at it. She can barely keep up in training, her classmates don't take her seriously, and the shadow of her father's legacy weighs on her more than it helps. But humanity is facing extinction from an alien insectoid race called Space Monsters, and Earth needs every pilot it can get. When the grizzled Coach Ohta selects Noriko alongside the school's golden girl, Kazumi Amano, to pilot advanced mecha units in the fight for survival, nobody's more surprised than Noriko herself. This 6-episode OVA from Gainax starts out almost deceptively lighthearted: there's sports-anime-style training montages and comedic moments that feel straight out of Aim for the Ace. But it gradually shifts into something heavier. The series uses real physics concepts like time dilation to explore what it actually costs to fight a war across interstellar distances, and those emotional consequences hit harder than you'd expect from something this short. The 80s soundtrack genuinely slaps during both the action and the quieter character moments. If you've watched Neon Genesis Evangelion and want to see where Hideaki Anno cut his teeth as a director, this is it. Fans of Space Battleship Yamato will also find a lot to love in the grand-scale space opera elements. It's only six episodes, and it earns every single one of them.