If you prefer realistic games then you might just want to pay attention to deals through Steam, which occur pretty frequently. You could probably pick up Counter-Strike: Source for $10–20, although that game’s number of players has depreciated lately.
There was one weekend I picked up Team Fortress 2 for $5, which is a great deal. TF2 has cartoony graphics, nothing like MW2, so I don’t know if you’d be into it. But it’s a lot of fun and easy to learn. You may want to check it out.
Strictly free stuff is understandably kind of limited, although I’ve played the free game Warsow and it’s a really enjoyable (and graphically attractive) variant of the typical Quake scene. It’s also a small game and doesn’t take up much space on your computer. The learning curve is a little high, though, and obviously there won’t be nearly as many players as there are on MW2 or even CSS.
I’ve heard a little about Gunz: The Duel, but I had trouble installing it so I can’t give you anymore info than the site can. It’s third-person rather than first-person and also features swords, armor, and other RPG aspects. But it is both online and free, so maybe it will suit your needs. I guess you’d call it an MMOTPS, or Massively Multiplayer Online Third-person Shooter.
Hope this helps some. None of these games is too graphically intensive so your computer should be able to handle all of them. Good luck!