Woodfire oven how to get crust soft and tasty
Italian pizza crumb must be soft (morbida, as Italians say) in its inner part (the one below the tomato sauce), and its outer rim can be more or less crispy.

You can check the requisite for being soft at this link from the Vera Pizza Napolitana association (check the "Description of the product"):


  The consistency of the " Verace Pizza Napoletana " - (Vera Pizza Napoletana) should be 
  soft, elastic, easy to manipulate and fold. The centre should be particularly soft to the 
  touch and taste, 
  
  ...
  
  The crust should deliver the flavour of well-prepared, baked bread.


The outer part can be crunchier or softer, depending on your taste. It will depend on the strength (W value) of the flour. You can check it in this Italian pizza flour manufacturer.

Using a longer fermentation time will extract more taste from the flour. That's why a crunchier outer rim is usually associated with tastier pizzas.

That long fermentation also helps the dough been extensible and not stretching back, which is desirable when you are shaping the pizza. I wrote more details on it in this answer on pizza flours.



In order to achieve a soft center, the pizza is done in a very little time (from 60 to 90 seconds). To get this, you need a very hot oven (over 450ºC / 900ºF). 

It is difficult to get a thermometer that measures that temperature (most infrared ones usually can't measure over 350ºC). You can check if the oven is too hot throwing flour in it. If it catches fire (in less than 5 seconds) then it's too hot. If it just gets dark, then it's ok. After using this method, remember to remove the burnt flour, or it will give a bitter taste to the pizzas you'll later put on it.

To get the outer rim of the pizza rise like bread, you should have some flames in the oven. They will radiate a lot of heat, so you have to rotate the pizza 180º during its baking, so it will get done equally in all the border.

The flames should be in one side of the oven, never at the back. This way the air that enters to feed the flame will induce a rotating whirpool that helps the air in the oven to be hotter.

As the floor surface of the oven is very hot (>400ºC), the pizza you put in it won't actually be touching it: it will be floating on its own steam. That's why the bottom of the pizzas are not burnt.



You are asking about adding sugar or not.

Sugar is the food yeasts eat. 

Flour has no sugar. But it has starches, which are molecules made of many sugar molecules together. Flour also has enzymes that can break the starches in sugar molecules. That happens when you add water to the flour, and the enzymes can move easily to do their work. But they need time to do so.

When you add flour, water and yeasts, the late ones have to wait a bit for their food. If you add sugar, they'll have food since the beginning (the sugar you added) to the end (the sugar from broken starches): sugar is added to make the dough fermentation in less time.

So, if you want a quick risen dough, add (a small quantity of) sugar. If you want a tasty one, don't.