If you want to check out some old-school anime (like,...old old...) try:
Robotech (English-language rework of three different anime [Super Dimension Fortress Macross {{1982}}, Super Dimension Southern Cavalry Cross {{1984}} and Genesis Climber Mospeada {{1983}}. The English-language story is very, very different from the originals, but still very good, and was completely different from everything else available in English at the time. After that, maybe check out the originals...)
Space Pirate Captain Harlock from 1978. Try to avoid the one that's called "Captain Harlock and the Queen of 1000 years" it's a mashup of two different anime, and they don't fit together well. There was also a fully-cgi movie made in 2013.
Star Blazers ...an English-language reworking of Space Battleship Yamato.
Mobile Suit Gundam (1979)
Kimba The White Lion (1965...with several sequels and remakes up to 2009)
These are the anime I grew up with as a child, and while some of them are kind of old-fashioned, they are still good stories.
