Comedy:

• Asobi Asobase - three girls form a school club so they can laze about, hijinks ensue. The artstyle radically changes every now and again, sometimes to straight-up horror-looking stuff, and the voice acting is amazing. https://www.youtube.com/watch?v=BQr0iZwNLOs However, seeing as you're getting into anime, I'm not sure if it will be as funny if you have no awareness of the tropes of the subgenre. Anyway, here's another great scene, with amazing mixing of Japanese and English to the background tune of a shitty recorder version of the US anthem https://www.youtube.com/watch?v=wcLsH9ROgfo

• Nichijou - very weird style of comedy, but hilarious. If you've ever wanted to see a school principal in body armor suplex a deer, this is the series for you

https://www.youtube.com/watch?v=Z7Et0a8fnuw

https://www.youtube.com/watch?v=byDglOhxmdA

https://www.youtube.com/watch?v=z30Y572EmCk

More serious stuff:

• Revolutionary Girl Utena, which was already recommended a bunch of times. Genuinely amazing series.
• Violet Evergarden - I'm not sure if it necessarily qualifies as "imaginative", but it was very effective emotionally - I cried pretty much every episode. In fact, I just looked up some scenes on youtube to link and started tearing up again. However, it's not exactly a sad or depressing series, I'm not sure how to describe it, but it's a very cathartic kind of crying. Some people complain about it being melodramatic, but I dunno, I loved it. The protagonist is a former child soldier who becomes a ghostwriter of sorts - the setting is in a weird position where it's seen lots of technological development (seems to be roughly post-WW1, with the exception of the protagonists's mechanical arms which are kind of steampunk), but a lot of the population is still illiterate, facilitating an industry of letter ghostwriters - you go to the post office, and there's people there who can write your letter for you. The whole series is also just visually beautifull.
• Texhnolyze - a post-apocalyptic dystopia, with the remains of humanity living in a crumbling underground city. In contrast to the above, this actually is a very sad and depressing series. It's very slow paced, and incredibly dark and hopeless. I watched it some time ago, but IIRC it took like 2 or 3 episodes for the protagonist to even start speaking in anything other than pained grunts, and there was a several-minute scene of him struggling to climb up some stairs. Probably not for everyone, but it is in a class of its own. Also, it might actually fit pretty well with the current vibes of looming climate catastrophe and imperial decay, but I haven't rewatched it recently to confirm.
• Ergo Proxy - another future dystopia, starring Amy Lee from Evanescence for some reason - humanity survives in domed cities, with the world outside of them being a wasteland. They have robots called AutoReivs, which keep becoming self-aware and causing trouble. Various conspiracies and dark secrets about humanity's life in the domed cities are revealed. Lots of philosophical references get made, including people saying 'raison d'etre' many times, so people occasionally deride it for being pretentious, but I think it's alright.
• Ghost in the Shell: Stand Alone Complex - one of my favorite animes. The GitS film is a classic, but I personally prefer the series. It's structured kind of like a police procedural, with a conspiratorial plot being slowly unveiled. Lots of great philosophy, cool transhuman stuff, occasionally neat political stuff (there'a state literally called 'The American Empire' in the lore, which, it turns out, did a bunch of imperialism and outright terrorism in South America), it's one of the best cyberpunk works in my opinion. Well, it's actually sometimes labeled as post-cyberpunk, which is a genre that may or may not exist depending on who you ask, but it's precisely the deviations from typical cyberpunk fare which make me like it so much.