Try out the demo for Avernum or geneforge,
here. They are pretty simple, but if you like them, you'll like them a TON. It's really either yes! or noooo! for those.
The Fallouts are great too - 1&2 really shine, but remember that they have to be patched.
If you haven't played them, the two first Diablo games are gold. Tons of hacking zombies and skeletons and demons and whatnot to pieces. Great, great!
I'd also like to recommend you to
this thread, Blood Bowl is a bunch of fun.
If you like something a bit faster, Cave Story is a great, free game. Seriously, it's got everything that a 2D sidescroller can have, I love it to bits. Google is your friend.
There's also quite a few excellent stratergy games. I'd suggest finding out if you prefer RTS (age of empires, Warcraft 1 through 3) or turn based (civilization). If you've got that one down, there's a lot of fun games in either genre.
Morrowind also shines like a fucking diamond, one of the best RPGs that's a bit more recent than Fallout and System Shock (another great FPS/RPG), but I think your computer can take it on.
Screens, since I'm a nice guy:
Avernum 2 (all the games look pretty much like that)
GeneforgeFallout (I think this is number two)
DiabloDiablo IICave StoryAge of Empires
One,
two and
ThreeWarcraft
One,
Two and
Three.
Civilization
Three and
Four (if you haven't played them before, you really don't want to try 1&2; too old)
Morrowind, also in [ulr=http://i180.photobucket.com/albums/x227/JethroVegas/morrowind9_640w.jpg]Third person perspective[/url]
That's a few. Should take a couple of years to finish.
^^