I've tried some different pizza dough formulations and baking techniques, though very few compared to many posters here. For something I know works right for me every time, which may be helpful to newbies, here is my basic Lehmann recipe for 2 pizzas of approximately 13" diameter. I don't have a mixer. I have a pizza stone, a wooden peel and a pizza screen (the screen is helpful, but not required). Oh, and perhaps the most useful gadget of all: a food scale.
Cold "yeast" pizza dough fermentations strike me as essentially the same thing as "no knead" bread, with which I've had great success, though I use a sourdough starter for that. It isn't necessary to work the dough very much by hand. Time does the job.
My usual NY pizza dough (makes two 12.5 to 13ish" pizzas):
480g King Arthur bread flour
300g water (bottled usually)
3/8 t IDY
1 1/2 t salt
1 t oil
Plus a little bench flour while kneading.
I weigh out 480g flour in one bowl. 300g water in another. I add the yeast to the water and stir. Add salt to the flour. Pour about half the flour into the water and stir with a fork. Cover and let rest for 10-20 minutes. Then add the oil and mix well using a fork. Work in the remaining flour. When it comes together briefly knead. Gluten development isn't important here, as that will happen in the fridge; just thoroughly mix. If the flour stiffens too much while kneading, cover and let it rest a little while and then continue kneading. Divide into 2 portions, place in lightly oiled plastic bowls. Cover and refrigerate for 2-3 days.
Set bowls out on counter roughly 2 hours before bake time.
I use just shy of 8 ounces of cheese per pizza. So far, I prefer a combination of mozzarella and provalone. I still haven't measured how much sauce I use, though I should.
I bake in my old gas oven on a stone preheated at 550ish for an hour on the bottom rack for about 4:45, then move up to a screen on the top rack for another couple minutes to finish the top. I almost always have mushrooms and other moist toppings that benefit from the extended cooking/drying time. I intend to experiment with partially drying mushrooms in a dehydrator. Pre-cooking doesn't provide what I like.
When the first pizza is done I set it (along with the screen) on top of the stove burners to vent/rest while I make the next pizza. I move the pizza to a pan or baking sheet lined with paper towels when I need to use the screen for the next pizza.
I have only limited experience baking in other ovens, and as most know, ovens are a big YMMV factor. Quite some time ago when my oven was on the blink I used a newer oven across the street. That was fun. Make up a pizza and run it over to the oven. Same stone. However, this newer oven topped out at only 500 on the dial. Pizzas weren't nearly as good as baked at 550 in mine. Just not quite enough heat.