Hey Ron. IN your situation you would use either:
A) Standard TV
B) PC Monitor using an XRGB (any of the family) to convert the PS2 signal to a high quality signal.
However, the PS2 isnt a great source to make an Arcade cabinet out of, unless you simply want to play PS2 fighters with arcade controls and use those midway classics collections.
Most people here will use a PC and run MAME and other various emulators, or they would use a modified Xbox and run mame and other emulators from it.
BTW, welcome aboard the boards.