Like Tyler said, Definately get the Pioneer A03 or A04... They are both PROVEN to burn PS2 dvd based games... Use Primo DVD for the software....
Also, use a seperate CD burner to burn your PS2 cd based games.. Would HIGHLY rec. getting a 100 % Clone CD compatible burner and use Clone CD for your CD burning software....
You can find the list of supported Cd writers on this website:
Clone CD supported writers.