Two Dangan Ronpa ones. To be honest, I'm actually just neutral on both songs, but I thought both were really used well (the first is one of the few where still images are actually used well, second goes nicely with Junko's attitude). Sadly this site only allows one video per message so it has to be two.
Marina and the Diamonds: Girls
Lady Gaga: Applause (mega spoilers but no one seems to worry about those in Dangan Ronpa anyway)
That's actually a pretty good description of it. Though, Gate Keepers is relatively obscure. It is one of the shows I watched back in the 90s and it does share a lot of similarities with this. I should watch it again, I still have the whole series on DVD, and I never did get around to the sequel.
I didn't care for the character design of Charlotte at first, but it grew on me. The eyes seemed kind of off to me, but the rest of the art is good and the overall animation quality is consistent. The backgrounds and set pieces in particular are well done, it's a good use of CGI without looking too much like CGI. You know it when you see it, but it blends in well with everything else.
Plus, the characters are fun, the MC is a bastard, but not a horribly unlikeable one once the show gets going. Some of the others are the type you'll either find cute or irritating, the little sister in particular. She doesn't get a ton of screen time though, so it's not too bad if you don't like her.
The three episode rule works with this one, if you're not into it by the third episode, you probably won't care for the rest. There's enough foreshadowing that you can see where some of the big plot points are going by then. Stick with it for at least two, the first episode only sets up the MC really, and the real premise isn't really explained until the second ep.