The family is out of town, and I have a day off. You know what that means: test kitchen. I was looking at JW's pizza recipe, and even though I've heard this time and time again, I'm a slow learner. It starts and ends with the dough. You'll either have a pleasant experience, or it will be misery and toppings will burn in the bottom of your oven. This is not a post to say that the previous one is at all incorrect, quite the opposite. But it does require some trial and error.
Think about what all of the ingredients in the dough actually contribute.
Flour, oil, and water: the basis of the dough. This can be 5/1 bread flour to corn meal or semolina (Jamie Oliver), or all purpose with wheat flour and semolina (JW). Or any combination. Again, trial and error.
Yeast: fluffy dough, elasticity. The more elastic, the MORE DIFFICULT it is to make it thin. About 3 cups flour per packet of yeast, or 1 packet per 4 individual pizzas. Think "Feed the Bitch!" from Bourdain's Kitchen Confidential. If you haven't read it, don't wait.
Sugar: fuel for the yeast. This can be done with white wine (Mario Batali), honey (JW), sugar, etc. Or, you can leave this out. It depends on how long you plan to let the yeast rise and how dense/thin you want the crust.
Salt: flavor. Everything is better with salt.
Rising time: fluffier, but more elastic dough. Fine for focaccia (pretty much the same recipe), some advocate the double rise which works well.
Kneading: activates gluten which I think makes the dough less dense, and more fluffy. That's why the recipe before says leave it in the mixer for the prescribed time, even if it looks like it's done. Too much kneading: light and fluffy, more resilient. Too little kneading: thinner, but can stretch out wider and thinner. The only problem is that it will have a dense cracker consistency that can be a little tough. Consider that Batali's (and probably anyone else's) homemade pasta recipe calls for kneading the dough at least 5 minutes or so. Even though there's no yeast, it still makes the pasta lighter and silkier.
So you have to find the right balance of your ingredients. And that all comes with what your particular taste, expertise, patience, ingredients, etc. It also makes a difference what type of toppings your considering. If you want pizza Margherita with fresh tomato, that's going to be wet and it's going to be hard to get it off the peel. Your dough and your cooking technique have to match to provide a nice, dense crust that will stand up to the soggy ingredients.
Consider how baguette or tuscan country bread is made. Can be a super hot oven, but it has to be dead even heat above and below to cook from all sides. In the case of the baguette, it's partly the steam from the water that they throw on there, and it's also the oven. In the case of country style bread, it's the brick oven.
I have trouble with a combination of wet and dry ingredients, and I can't get the pizza off the peel onto the oven or grill stone without slinging all of my toppings into the bottom of the oven and having the whole house smell like burned cheese or chicken. You could put parchment paper down on the peel and then put the dough on that, putting both your pizza and the parchment paper in the oven on the stone. I suppose there's no reason you couldn't also use foil. Dough isn't done but the toppings are almost burned? This one, confuses me. I know that you can turn the temp down and balance that, but how then, do the Italians and various restaurants cook it in a scorching hot brick oven? It's because they do it in a brick oven that provides perfectly even heat on all sides. One side being done before the other is a case of uneven heat.
The key is to experiment, and I think JW is right: with several trials and errors, umcompromising quality of ingredients, and a tenacity to learn how to do it, you can probably make pizza at least as well as anywhere you can go buy it. Trial and error is the substitute for learning it from your Nonna....and you can learn to do it many different ways.
Final note: really want to cheat? Pepin describes using flour tortilla to make pizza. Haven't tried that one yet, but it just might work! Although, I don't think you'd call it pizza.