You can download the emulator from this site or
www.pcsx2.net.
There is no compatibility list as such, as 99% of games do not work!..or those that do go ingame run at less than 4 FPS

PS2 emulation is in it's extremely early stages, and machines simply are not powerfully enough to achive full speed.
I would recommend trying:
Guilty Gear X
Super Bust a Move 3000
Street Fighter EX3
Police 24/7
Namco Museum
as they are all playable to some extent