I also vouch for HL2. To bad you don't have a credit card, if you download Steam from
www.steampowered.com, it's free, install it and run, I think there is a free game or two, and perhaps demos that can be played. With a credit card you can buy a "package" which includes HL2 and source mods and lots of other variants. If you buy HL2 off the shelf retail, you may get less games.
I don't even play CounterStrike, I just like Half Life and all the mods that are out there! I play single player over and over. Call me a monkey.
As for MMORPG, the favorite in my circle of friends is Lineage II. Not the for-pay retail, but all the free servers out there. Namely L2World and L2Dragon. And also the server that is run by my friend (it's small now and not a ton of members, great for getting started) is L2nxa. Check out l2nxa.com. You can download the client (all free) which is about 2gb in size. And then create an account, free also. And play, free. To play on many free servers, you can mod the game client, or just install multiple copies of the game for each server you play on.
In my opinion, it has way better graphics then WOW or Anarchy or Final Fantasy and so on. Visit the official Lineage II web site
www.lineage2.com for screenshots, videos, demos, info and everything.
Really, to spend all day and night playing games, all you need is HL2, Lineage2, and Battlefield 2. Cause you know, the number "2" is so fun.
And speaking of BF2, also good fun, but I'd put CS:Source and BF2 online play in totaly different categories. In BF2, you can hardly run solo, it is very much a team based game, and it would be good to get yourself in a clan eventually. But at the least you'll have to learn how to play as a TEAM to get anywhere.
Anyway, info overload, but those are my tops choices. Then I'd add the classic Total Anihilation to that, can be played in a LAN party, or single, still great fun. And that my friend, covers the 3 main game classes: FPS, MMORPG, and RTS.
Have fun.