I've been a fan of Matsumoto Leiji ever since I saw Dangard Ace many years ago, as well as Galaxy Express on Sci-Fi channel when they showed anime on Saturday mornings. I don't know why it took me so long to watch this show, but I highly recommend it.
This right here, the entry for Space Battleship Yamato, is the original series from which the '77 movie was derived. It fully chronicles the adventures of the crew of the Yamato, born from the wreckage of the WWII battleship, the last hope of Japan, or so it comes across that way in the series. I'm not sure how that was adapted when the show was made into Star Blazers, but I'd like to find out.
All the names I use here are the ones from the subtitles in the version I watched.
By the year 2199, Earth has been under constant bombardment from the planet Galimus for several decades. From their front line base on Pluto, they launch meteor bombs daily at the surface of the Earth, which has destroyed the surface, driving the entire populous into underground cities. But this does little to save the human race, as the meteors also spread a radioactive poison, which is slowly but inexorably seeping down into the crust. Their last hope (perhaps reflecting the feelings of Japan at the end of the war, or maybe not) is the first earth ship capable of faster-than-light travel, the Yamato. Launched in response to a message from Starsha of Iscandar, sister planet of Galimus, their mission is to retrieve an item called the Cosmo Cleaner, which can eliminate the poisons spread by the meteors. But, at the time of Yamato's departure, the amount of time mankind can survive is exactly one year. With out any help, can the crew of the Yamato travel the 148,000 light-years to Iscandar and back in one year, all the while being attacked by the space forces of Galimus?