PCSX2 is the best one i found.
http://www.pcsx2.net/
A LOT of games don't work(like God of War, Resident Evil 4,Gran Turismo, etc...) but some do. I can verify that Final Fantasy X works and it looks a heck of a lot better than running it on my PS2.
Because of the way that the PlayStation 2(and PlayStation 3 for that matter) is set up it really requires a
strong CPU more than a huge GPU.
I would say that minimum requirements would be:
Dual core AMD/Intel
Nvidia 7900/ATi x1950 or better
2 gigs of RAM
Preferable setup:
Intel Dual core or Quad at 4Ghz
Nvidia 8800GT/ ATi HD3870 or better
Over 2 gigs of ram
Also, make sure to download all the latest plugins also. You may find that not all the plugins cooperate with your system so it's really a hit or miss situation. Takes some messing around with it to get a good balance.
Here is a Beginners guide:
http://forums.ngemu.com/pcsx2-forum/101343-running-pcsx2-guide-noobs.html
And here is the official guide:
http://www.pcsx2.net/guide.php
Here's a compatibility list that's mostly correct:
http://www.pcsx2.net/compat.php?c=key
If you have any more questions feel free to post and i will answer the best i can with my limited knowledge of the emulator