Good old margherita.
I use the "pizzeria" flour from the company Caputo.
1kg Flour
600ml cold Water
40g salt
1/4 cube of yeast (or the equivalent in dry yeast, sometimes I use a whole packet)
Pre-Dough
I mix the cold water, salt and yeast and add half the flour (the half is super important)
Then I put a lid or wet towel on it and let it sit for at least 30 minutes (but optimally longer).
You should be able to see that pre-dough do produce get bubbly and produce CO2.
Dough
Then mix the rest of the flour in and knead that thing. Let it sit in the fridge for a day and then make 6 small balls out of the big one and put them into containers and into the fridge.
Oven
Its all about heat.
I use a G3 Ferrari pizza oven. They claim to do 400C (I think it's less) and can be had for like 60-70 €/$ and there are similar ovens from different brands.
My dream electric oven would be a used professional small oven that goes to 480C. I've seen them for 200-400 €
If you're using a regular kitchen oven get a pizza stone for nice results. An outdoor grill also works well with a stone.
Same! But I'm wondering if there's some science behind the circles, or am I ok to grate stuff on for more even coverage.
You'll find a lot of Italian chefs used julienned mozzarella/fior di latte, or batons, rather than big circular slices. There's no firm rule that I'm aware of!
That said, trying to grate fresh mozzarella, instead of low moisture mozzarella (like is generally used on non-Italian style pizzas), would likely leave you with a big wet smeary mess.
I make a dozen large pizzas a week (I do a weekly pizza night for our small cottage bakery) and I cut my fior di latte into strips, then let them dry out a bit, covered on a wire rack in the fridge overnight before using.
It's really hard to grate fresh mozzarella. It's very soft and moist. The circles are because it comes in a sort of cylindrical shape and people just slice off thin pieces.