The only two that I've listened to are S.M. The Performance and Girls Generation. Back in high school, I lightly dabbled in J-Rock and J-Pop, but I'd really like to broaden my musical horizons with some Korean music. I'm not too familiar with the K-Pop community, other than the fact that there are a lot of girls with certain "idols" that they obsess over.
Are a few good groups that I haven't seen posted here yet, If anything though I would for sure look into B.A.P., Block B, Big bang, 2ne1, Exo, U-kiss, and Super Junior. Those seem to be the big ones, at least in my little group of people.