If you aren't afraid of going back to several years ago gaming graphics, you have to give Starcraft a try. I think you can get the Battle Chest for it at Wal Mart for $20 now. Its challenging yet not so hard you get discouraged. Plus its a long game, espically with the Brood War expansion (comes in the battle chest).
I'm not sure how strong its online playing is anymore, but back in the day it was really fun to play online, also had ladder games which increase and decrease your ranking, and they have more strict rules. Battlenet has also eliminated 99% of any cheating that used to occur online.
I recommend you beat the Terran, Protoss, and Zerg campaigns before attempting to play online though, only knowing 1 race and playing online = defeat.