Gunbuster the movie is a compilation movie based off of the OVA Gunbuster (known in japan as TOP WO NEARE! (Aim for the Top!)). The movie was made by studio Gainax, who later made Neon Genesis Evangelion and Tengen Toppa Gurren Lagann and in director's chair sits Hideaki Anno, the same person who later directed Evangelion. Also this movie has a sequel known as Diebuster (AKA Top Wo Neare 2 or Gunbuster 2).
The OVA and the movie were made in 1986, so make note that this movie is cel animated instead of drawn digitaly so some of you might think that the movie looks not as good as today's digitaly animated anime (to which I respond with the suggestion of going back to your life of illegaly downloading Naruto fansubs). The hand drawn cel animation has a great charm that today's animation can't match. The art style also looks like the best the 80s can offer, really.
The plot seems to me like a mix of Go Nagai's Getter Robo, estrogen and a bit of Star Trek.
In the far off year of 2015 (keep in mind this was made in 1986), humanity has made giant leaps in technology to fight against aliens. Noriko Takaya, who's father was the captain of a starship that was destroyed by aliens, wishes to become a space pilot just like her father. Trained by a survior from her father's ship named Koichiro ''Coach'' Ohta and inspired by her uperclassman and big sister figure Kazumi Amano. Without spoiling much more, Noriko and Kazumi later on pilot the mecha Gunbuster for the sake of humanity.
The ending is pretty emotional too.
So the plot is kind of generic except for one thing. The movie uses the real life concepts of lightspeed travel and time dilapitation. So basicly, when you travel at light speed, time passes much faster in lightspeed than it does outside of lightspeed. What this means is that 5 minutes in lightspeed takes several months outside of lightspeed. In the final act of the movie this comes in to play when Kazumi, who was on earth for 15 years is in her 30s while Noriko, who was in lightspeed the whole time only ages by a year.
But then there's some flaws. I would have prefered to get the OVA instead of the movie since the movie omits several plots present in the OVA, such as where Noriko fights whatsherface in the school or the fight between Kazumi and Jung Freuid in space. Still, the most important plotlines remain, however sometimes the pacing is shot and for most of the time it seems like Noriko cries like every 5 minutes during the first half of the movie.
But the absolute weirdest thing about this edition of the movie (and probably the most important thing you should know, I suppose) is this. For the hour of the movie the game is not in widescreen and in color, but the final act of the movie is in widescreen and black and white which is kind of jarring.
So overall, the movie is great and worth owning. But if you get this movie, you must also get Diebuster since these two complete each other and make the experience even more enjoyable.