First up is the main character Nono. An enthusiastic and wide-eyed young woman, she dreams of going into space and joining the fight to protect humanity from the invading Space Monsters. She also happens to be an android who is strong enough to physically beat the crap out of space kaiju.
Next is Lal'C, a stoic princess and Buster Machine pilot who befriends Nono while kicking butt in her giant robot Dix-Neuf.
And finally there's Tycho, another Buster Machine pilot. Hotheaded and carrying some serious emotional baggage, she's initially jealous of Nono's talents but comes to see her as a friend.
The series has some really fun moments, but it requires watching Gunbuster first to really understand everything. The plot also gets very confusing at times due to lightning-fast exposition and only so much time to read the subtitles. XD There's also a fair amount of fanservice, which may or may not appeal to your tastes. But it's a very sincere show in its love for the over-the-top awesomeness that is the Super Robot genre.
