The amount of oil, and also the type, tend to be matters of personal taste and preference, although increases in the amount of oil should increase the extensibility (stretchiness) of the dough and maybe make the finished crust and crumb a bit more tender. However, for the NY style you perhaps don't want to go beyond about 3% oil. As for the type of oil, as best I can tell, most professionals who specialize in the New York style tend to use soybean oil, mainly because of the low cost although some may use a pomace olive oil as a low-cost olive oil option. It is also possible to use a blend of oils, such as olive oil and soybean or canola oil.
My advice is to play around with different possibilities until you find your personal sweet spot.