I'm in the same boat as you, I got my modded PS2 with the DCM9 chip this past Friday.
Once difference though, I got an outdated DVD burner off of Ebay for $38 + shipping. Everyplace I've seen recommends burning your game backup DVD's at 1x so top speed didn't matter.
But, to answer your question, you can start with some Emulation discs:
PGEN runs Genesis, and I created a Sega Genesis disc last night, it worked flawlessly. I've got all sorts of Genesis emulation on my main PC and in my cabinet, but there was something really satisfying about playing it on a TV with a controller.
IT MUST BE NES and SNES-STATION are nintendo emulators that I am going to fart around with tonight.
Other things to try...well, a lot of PS2 games are CD based so you can burn them on your cd burner, but you need to look into that yourself...
Hopethis helps!