Anyway, these are the PS2 games that I've played before and enjoyed:
Okami (definitely one of my all-time favorites)
Metal Gear Solid 3 (ditto)
==> try to get MGS2 to complete the story
Shadow of the Colossus
Katamari
Silent Hill 2
=> if you are fan, you can try to play SH3/SH4
they are not as good as SH1/2 but if you like SH it is ok.
Kingdom Hearts
Devil May Cry
God of War
==> maybe god of war 2 ?
Games that I don't like, even though I know they're popular and everything:
Grand Theft Auto
Final Fantasy or any other jRPG (giving XII a shot, because I heard it's different)
Racing games
Games I haven't played, but I'm looking into because they seem promising:
Ico
==> quite different that Shadow of colosseus even if I never played to SoC
for me ICO is not interesting enought ... try to rent it.
Ratchet and Clank
God Hand (Clover <3)
+
RE4 : it is a good game but it is not anymore a survival horror.
overall, since all htese games are quite short, you can rent them or take second hand game like me.
Time to Work !