I guess I would define it as more NY style than Neapolitan, in that it is mostly like NY style but still retains more of that bubly, floury quality that Neopolitan pizzas posses. I'm from southern california, and I cannot really think of any places which reflect what I'm imagining (and if I did... I'm sure few would know what I'm referring to). I'm looking for a light semi thin-semi medium thickness crust which has some chew, little crunch, while being cooked all the way through. Does this make any sense?
It sounds like you are talking about a basic NY style, using a pretty standard combination of flour, water, yeast and salt. A dough skin made from such a combination is usually on the thin side but some people like a thicker skin--maybe more like a NY street style. Some also like to add a bit of oil to the dough for flavor and other purposes (depending on the amount of oil used, but typically under 3% of the flour weight).
As for your basic question relating flour types to pizza styles, I would say that, as somewhat a generalization, all-purpose flour can be used for pretty much most pizza types. For example, I have seen all-purpose flour used for the NY style, American style, Chicago traditional (South Side) and deep-dish styles, cracker style, Sicilian style, thick style, and the California style. There are Neapolitan style doughs that have been made using all-purpose flour, or combinations of all-purpose or bread flour and pastry flour or cake flour, but such doughs are really only attempts to copy the Neapolitan style. An authentic Neapolitan dough requires using Italian 00 flours.
Although all-purpose flour is a generally useful flour as noted above, there are many other possibilities. For example, the New York style dough can be made using all-purpose flour, bread flour or high-gluten flour. In the early days of pizza making, in the 1920s-1930s, all-purpose flour was the most widely used flour for the NY style. Bread flour existed during that period (for example, in 1920 there was a Gold Medal flour called High Protein Flour, later to become the Better for Bread Flour), that no doubt was also used to make the NY style. However, high-gluten flour did not become popular for pizza making in general (it was widely used for bagel dough) until sometime in the 1970s-1980s. Today, I would say that high-gluten flour is the most popular choice for the NY style, especially in the NY City area. As you may discover, high-gluten flour is rarely found at the retail, supermarket level. For that reason, many of our members use a high quality bread flour. Some even prefer that flour over the high-gluten flour for the NY style.
The doughs for American style pizzas, as typified by Papa John's, Domino's, Little Caesar and Pizza Hut, generally are made using a high protein flour, either high-gluten flour or a proprietary high protein flour, which could even be a bread flour or something similar, milled and blended especially for those companies. It is not entirely clear what Pizza Hut is using. It has gone mainly to frozen doughs with a lot of additives that mask the type of flour used.
The most common flours used for the Chicago deep-dish style are all-purpose flour and bread flour. I don't recall ever seeing a Chicago deep-dish dough recipe calling for high-gluten flour. Even among bread flours, there is one that is considered to be the most authentic. It is the Hecker's flour, also called Ceresota in some markets. The Hecker's/Ceresota flour has a protein content of about 12.5%, which apparently makes it ideal for the Chicago deep-dish style. Its popularity may also stem from the fact that the Hecker's flour is a midwest flour that is readily available in the Chicago area. The traditional South Side Chicago style pizzas appear to use either all-purpose flour or possibly bread flour. Generally, the pizza places that offer both Chicago styles use the same flour and dough for both styles.
I would say that the most popular flour for the cracker style is bread flour or high-gluten flour. All-purpose flour can also be used but in my experience the top and bottom crusts, and especially the bottom crust, is not quite dark enough to suit my preference. However, you will find cracker-style dough recipes on the forum calling for all-purpose flour.
Neapolitan style doughs, specifically, those that are authentic Neapolitan doughs and intended to be baked in very high temperature ovens, as is done in Naples, use the Italian 00 flour. That flour is best adapted to very high temperature ovens. It does not perform with anything approaching the authentic Neapolitan style when used to make doughs to be baked in a standard home oven. If 00 flours cannot be found for any reason, flour blends attempting to simulate 00 flours can be used, as mentioned above, but they will not be authentic.
You will sometimes see combinations of the Caputo 00 flours with other flours to produce what one might call a "hybrid" flour. One well known example is Dom Demarco's use at Di Fara's of a 75/25% blend, by volume, of Caputo 00 Pizzeria flour and high-gluten flour (quite possibly the All Trumps high-gluten flour). In his case, he uses an old gas-fired oven (Bakers Pride) that operates at higher temperatures than most commercial gas-fired ovens.
Sicilian doughs can be made using either all-purpose flour, bread flour or high-gluten flour. Most flours used to make this style commercially are bromated flours. The bromates (potassium bromate) help retain the height of the dough during the final proof before baking, which is highly desirable for this style of pizza. Some people prefer to use a high-gluten flour because of its stronger gluten structure and its ability to produce good height and gas retention. However, it is doubtful that the Italians who invented this style (sfincione
and its variations) used high-gluten flour. All-purpose flour or its equivalent based on their national grains were/are most likely used.
The traditional California style doughs tend to use mostly all-purpose flours, although using a whole-wheat flour in combination with all-purpose flour is also common. Apparently, doughs made form these flours seem to work best with exotic cheeses and toppings. No doubt, in certain cases, bread flour can also be used. The dough recipes in the California Pizza Kitchen Cookbook
call for the use of all-purpose or bread flour. There is also a whole-wheat/bread flour version.
Whole wheat flour, whether the regular whole wheat flour of the "white" version, and other flours like rye flour, are typically used to make what we call on this forum "Specialty-Grain Pizzas". Often, the whole wheat flour is combined with all-purpose flour and sometimes with vital wheat gluten. You might see a reference here or there to a "whole wheat NY style" or a "whole wheat deep-dish style", but those applications will usually be someone's adaptation of those styles. Increasingly, however, pizza operators are adding whole wheat pizzas to their menus.