Signus, for NY style, pasta sauce is generally cooked, pizza sauce is generally uncooked.
In it's simplest form, NY style sauce is just a good tomato, salt and, unless the tomato is extraordinarily sweet, it almost always requires some sugar. You can put the oregano on top of the pizza or in the sauce. A tiny bit of fresh garlic (a little bit goes a long way) or some finely chopped fresh basil are nice additions, but not essential.
Most puree is reconstituted previously cooked (bad) paste, and the non-reconstituted purees generally can't hold a candle to the taste of less processed tomatoes. The pizzeria of my youth had access to better puree than I have access to now. To match that flavor, I find that I have to go with a ground tomato. The 6 in 1s are solid performers, but I think it's possible to get a ground tomato at a supermarket. Some Walmarts have the Classico ground peeled tomatoes- those have a good track record.
Your best bet is to buy a variety of brands, taste them, and see which one comes out on top.
The one downside to ground tomatoes for you is that the texture can vary, and, because they have seeds, you don't want to blend them, as the seeds will turn the sauce bitter. Some brands can be on the smooth side- not puree smooth, but not chunky. At the same time you're testing for taste, look at the texture as well. If the seeds are not too numerous, you might be able to get away with a little hand blending, but I wouldn't blend it too much.