While Starcraft is a good game, it is a bit outdated. I would recommend Warcraft III if you are into RTS games.
Counterstrike is an excellent game. Yes the online people can be irritating or downright rude, but that is true for any game you play online. I wouldn't play an online game unless you have really thick skin.
Personally, I prefer online RPGs and strategy games. Currently playing Guild Wars.
"And so he spoke, and so he spoke, that lord of Castamere. But now the rains weep o'er his hall, with no one there to hear." - The Rains of Castamere