Cowboy Bebop is what kicked it off for me. Outlaw Star was a lot of fun, but coulda used more cowboy style shit on the soundtrack. Watching Space Dandy now and while it's not quite a space western, it's pretty fun to me.
Anything else I should check out?
Not sure if that's good enough for the criteria, but Space Battleship Yamato is very good and it has a 2010s remake. And if you're looking for something that doesn't take itself too seriously, The Irresponsible Captain Tylor is one of my all time favorites: it's 1/3 a sci-fi parody of space operas and shows like Star Trek, 1/3 a serious space opera and 1/3 anarchist propaganda.
That latter one sounds fun as fuck!
Disclaimer: Episode 1 is the worst of the whole series, but from E2 it's consistently good.
Space Battleship Yamato (1974) should be mandatory viewing for any sci-fi anime fan.