I don't know too much about it, but you could go the hdd route if you don't want to do the modchip or Swap method. Basically, you install a hdd to your ps2 and you load your games onto the hdd to play them, might need dvdloader or cdloader to play those i think. But those are free to download i think.
PS2 games are actually pressed DVD/CD discs, they are not burned. PS2 games use the Burst Cutting Area (BCA) of the disc to identify themselves to the PS2 unit. The BCA is not part of a disc that you can burn on, it is only replicated on pressed discs. So, the only way to play backups is to get boot-discs or a mod-chip.
Now for a modchip, The ps2 has VERY SMALL POINTS,
It takes a high amount of soldering skill to add
a modchip to the ps2, if your going to try then
Also i suggest getting a 15W soldering iron, no-corrosive flux, de-solder braid, and a 0.1mm iron tip. As well as 30 AWG kynar wire and 22 AWG wire for the ground and 3v3 connections.
Dvd decrypter will copy and burn all your backups,
Get some quality media (4x max -r media)
And burn slow as possible.
