But the list is great and no I don’t mind sci-fi at all. I’ve just caught up with all 182 ep of Gintama (yay!) and sorta “finished” Toraburu/ To-Love-Ru and the old Full Metal Alchemist. By finished I guess I mean watching and or marathoning episodes until I get bored with too much of the re-running side gags or present storyline and then I wiki up the ending. Haha. I guess I’m an impatient person. But I guess I’ll start now with Lupin III. Thanks so much for the tailored list, esp since the non-slice of life and love triangles is a bit of an odd filter. I’ll let you know how the animing goes!

Mobile Police Patlabor: One TV series, two OVA series, a couple of directly-related movies and one movie that doesn’t really relate to the series in any way. On the surface, it’s a slapstick giant robot show designed to sell model kits, but the creators managed to hide a lot of rather intelligent themes under the goofiness, mostly dealing with humanity’s increasing dependence on technology and how it interacts with the rest of the world. The division commander, Goto, is probably the anime character I’d most like to be like.

Lupin III : The Castle of Cagliostro.
You mentioned Nausicaa as a landmark animation, so I’m hoping you’ve seen this, one of Miyazaki’s earlier films. If you haven’t, it’s very much worth watching. Much like Urusei Yatsura: Beautiful Dreamer, this is an example of what happens when you take an existing set of characters and hand it over to a genius director; it’s not entirely Miyazaki’s work but he put his personal stamp on it.

Irresponsible Captain Tylor
Now, this has a bit of a love triangle aspect in it, but it’s pretty low key; the main character is a hapless and clueless doofus who rises from being a complete nobody to being, well, commander of a battleship and beyond solely by being friendly, personable, charming, and stupid. Mostly stupid. On the other hand, nobody can quite decide whether he’s really THAT dumb or whether he actually has a plan…
Goes from a very silly opening to a very serious ending.

Martian Successor Nadesico
It doesn’t seem right to bring up Tylor without bringing up the other classic parody-or-is-it? space warfare anime; Nadesico is a goofy sci-fi anime, with characters who are themselves fans of an even goofier sci-fi anime from their youth, and they’re out to save the world from a malevolent and faceless alien race. It’s hard to explain more without spoiling one of the series’s major plot twists, but it’s one of those shows that works on several levels; the farther back you sit from the events, the more serious it gets. Addresses very heavily the concept of what makes an The-Enemy-As-Other, and how taking situations as black-and-white can backfire in catastrophic ways.
There’s a movie; it doesn’t make sense because it’s a sequel to the story of a Sega Saturn game that was never released in this country.

Gall Force (1, 2, 3 & Rhea)
OK, it was the mid 80s and companies were riding the wave of the new OVA craze, so you’re going to have to excuse the occasional bit of gratuitous nudity in this series.
Gall Force is one of those series that has an intensely depressing premise; it’s a war between two races that have been fighting for so long that neither of them remembers the reason behind the conflict, and both have been diminished to the point where they reproduce solely by cloning. The situation is, frankly, bleak for both races and neither one has any hope of “winning”.
Even with that, the series has an overall very optimistic theme.
The modern show I most compare it to is the recent “Battlestar: Galactica” remake; if you’ve seen that I’d be curious to know if you see the same parallels I do.

Revolutionary Girl Utena
Based almost entirely on your list of suggestions, I’m going to say that you need to see this as well, though I’m going to bet that you probably already have. Girl goes to an exclusive academy, gets sucked into a mysterious dueling circle, winds up “married” to another of the female students, discovers that the school is, well, very very odd indeed. Amazing music and an art style that looks very odd in stills but incredible in motion. There’s a movie in addition to the TV series, I don’t recommend the movie but I have seen other people gush about it so I may just have bad taste.

Magical Stage Fancy Lala
OK, this anime was aimed at grade-school-age girls, so it doesn’t exactly get gritty. It’s one of several magical girls shows put out by Studio Pierrot, all of which follow the same basic plot: Perfectly ordinary, basically invisible girl gets the ability to transform into beautiful older girl, older girl gets famous, this is fun and exciting but comes with problems of its own. All of these shows end in basically the same way and deliver the same message to their audience; I recommend Fancy Lala because it came out several years after the other shows in the same vein and is more watchable by modern standards.

Nadia of the Mysterious Seas
Studio Gainax’s first TV show, it starts off as a light-hearted adventure romp and gradually gets more serious. The main characters are a technology-obsessed nerdish kid and an Exotic Girl With A Mysterious Past Who’s Being Chased By Evil People Set On World Domination, but that plot wasn’t quite as much of a stereotype at the time so you’ll have to excuse Gainax for it. If you like Miyazaki movies for their antiwar, pro-environmental themes, you’ll probably like it.
Warning: There’s a arc about halfway through described as the “Island arc”; until I saw the Endless EIght it was the most painful thing I’d ever endured without actually giving up on a series.

Otaku no Video (2, 45 minute OAVs)
Another Gainax animation, essentially my generation’s version of Genshiken, just set in a time when being a fan was, oh, slightly less socially acceptable.