PS2 reads backups with a mosdchip. The best modchip to use is Messiah because you just put the backup in and boot without any boot assists.
Unless you want to get into complex ripping of DVD games ontyo CD (and this gets difficult as they exceed 4GB), you should take a Pioneer A03 or A04 DVD-R burner. Full totorials and download software at
www.psxcopyworld.co.uk.
For the diminishing ban of CD games, you's copy with CloneCD and no patching is required if your brnemer is 100% compatible supporting RAY-DA0+96 on reading/writing.