One of my favourite classics tonight;
Gunbuster.
Noriko Takaya is the daughter of Yuzo Takaya, a famous Admiral of Earth's space fleet.
Adminral Takaya perished battling the Space Monsters (no other name for these creatures were given in the series, and Noriko tries to follow her father's footsteps.
She is met by a lot of resistance from her peers at the Space Academy, but is chosen to join Kazumi Amano to go to space and fight the Space Monsters with the Gunbuster machine, a giant robot made for this effort.
Gunbuster isn't as much a mecha-show as it is a tale about believing in one's strength and to overcome one's fears.
Another thing I really like about this show is the way it uses certain theories regarding Star Bows and the Rip van Winkle Effect when travelling at (sub)light speed.
A couple of minutes travelling for Noriko means that 6 months go by for those who are left behind on Earth, and the impact of this leaves it's marks on her, as her friends grow older while she remains in her teens due to her travels in subspace.
The show also has its share of jokes to take the edge off, and the whole series (Gunbuster is a 6 episode OVA) is a pleasant show to watch in one go.
If you're looking for a classic, go and see this.
Cheers, K.