Black Rock Shooter has rad fight scenes with cool girls like Kill la Kill does, along with some intense emotional stuff. There's an OVA and a TV series. I would recommend watching the OVA first.
Mekakucity Actors has like super power / supernatural abilities with some comedy and emotional things. There is also a manga. It can be really confusing for some people, though. If you plan on watching this, I would also say watch the
music videos that go with this anime before or after watching / reading it.
Puella Magi Madoka Magica is a psychological and dramatic anime with cool fight scenes and very interesting animation. It involves magical girls, but don't let that fool you because it is jam packed with feels. When I first watched it I thought, "Hey, this art style and concept is really cute. I'm sure nothing bad will happen." A few episodes later, and I'm like crying internally. This show also has a movie called "Puella Magi Madoka Magica: Rebellion". It's a sequel to the first two movies, which are just recaps of the show with improved animation.
Watamote is a comedy anime featuring an antisocial 15-year-old shut-in girl. It has lots of cringy and secondhand embarrassment moments. It doesn't really relate to any of the shows you listed, but I think it's still worth the watch.
Angel Beats is another one with cool animation and awesome fight scenes. It's pretty emotional as well. It's about a kid who wakes up and finds out that he's actually dead and trapped in the afterlife with a bunch of other people. You get to eventually learn how these people died and why they are in the afterlife.
