Both TF2 and BC2 are great, and between them they are $50 ($20 for TF2 and $30 for BC2), so you could probably get both, since they are the price of one new game.
As for other FPS games, you could go with Call of Duty 4 or it's sequel, Modern Warfare 2, both of them have strong online communities, and are just plain great games.
For RTS games you could go with Company of Heroes, which is in my opinion the greatest RTS game of all time. If you only want to play multiplayer, go with the Tales of Valor stand-alone expansion, that has all the online content from every game in the series, but doesn't have the single-player component.
Plenty of great games out there, and most of them are quite inexpensive, too.