everybody has different tastes for their PS2 games. So I suggest YouTube reviews made by various people. You didn't say what kind of games you are into. here is a link to a bunch of PS2 reviews to help out some. because for myself I favor First Person Shooters, Sports games and Arcade Compilation ports over RPGs, Platformers
https://www.youtube.com/results?search_query=ps2+reviewsAnyway I highly recommend if you don't mind mostly 1980's and early 1990's arcade games also early 1980's atari and intellivision
1: Capcom Classics Volume 1
2: Capcom Classics Volume 2
3: Midway Arcade Treasures 1
4: Midway Arcade Treasures 2
5: Midway Arcade Treasures 3
6: Taito Legends 1
7: Taito Legends 2
8: Mega Man Anniversary Collection
9: Megaman X Collection
10: Atari Anthology
11: Activision Anthology
12: Intellivision lives
13: SNK Arcade Classics Vol. 1
14: Namco Museum: 50th Anniversary
15: Sonic Mega Collection Plus
These games are good starters because they all contain multiple games per purchase