While it's not completely related to your previously watched titles, Ghost in the Shell and Ghost in the Shell: Stand Alone Complex. The '95 film and the first season of the TV anime are essential. Innocence and 2nd Gig, less so.
Allow me to reiterate: ESSENTIAL.
However, make sure you watch the original version (ideally in HD) in Japanese with subtitles. No, I'm not one of those purists. In this case, the dub is simply bad. Furthermore, the "2.0" re-release only adds intrusive CGI. Not worth it.
The Stand Alone Complex dub is apparently good, that one is up to you.
EDIT: Forgot to mention that there is nudity in the films, I don't know what your club's policies are on content (or if you're in High School or college), so you may want to take that under advisement. Mind you, it isn't fanservice. Mamoru Oshii plays it pretty coldly and often in combination with mechanical bits and bobs, making it feel more like a scientific look on a replacement of the human body. Stand Alone Complex does not have any nudity, yet it somehow has more fanservice (still less than, say, anything by Gainax).
That's how it seems to me, anyway. Others may watch it and conclude "YAY TITS", and that's fine.
Anyway,
K-ON! sounds like the kind of thing you'll like. Definitely the best moemoe slice-of-life show. Why? It's actually funny.
Ichigo Mashimaro is another great slice-of-life show. If you can get past the ultra-cute and somewhat suspicious exterior, it's very funny. The jokes are well-written, and there's real comedic timing.
Dennou Coil. More people need to see this one. A brilliantly-written mystery with some plausible science. No, really. Some of the things in this series may actually become real in the future, assuming there is a good market for AR technology.
