Um dude. Legend of the Galactic Heroes. It is seriously in competition for my top spot with BSG and B5. It is a little older (late '80s-early '90s) so it's not slick and flashy. It has no goofy anime conventions, and I mean fewer than Planetes and Cowboy Bebop. It is straightforward, pure space opera with no aliens or magic or time travel. Most of the characters are over 30, all of them are realistically proportioned and, more importantly, written. It's a conflict between two great space powers in separate spiral arms of the galaxy. One side is a failing democracy, and the other is a reforming totalitarian state - there are heroes and villains on both sides.
It's more about the characters, the plot and strategy, and political wrangling than the battles - but they dwarf those of B5 and Star Wars, and usually are big fleet standoffs with fusillades and barrages and tactical planning, rather than ship-to-ship melee combat. Every piece of music besides the opening and closing themes, and the two national anthems, is classical music, as in Mahler, Beethoven, Tchaikovsky, etc.
I can not talk this series up enough. It's never been licensed for the US, so fansubs are the only way you could watch it, but Central-Anime has finished the 110-episode main series, and is (slowly) getting through the prequels, which you would want to watch later anyway.