Storing pizza dough
If you need to go shopping for pizza toppings, just stick the bowl in the fridge until you come back. You can even store it overnight, which a lot of people think adds flavor to the dough. Bring the dough to room temp when you are ready to make the pizza.
There's really no problem to balling up the dough and sticking it in the fridge. You can leave it in the bowl, but I prefer wrapping it well so it doesn't develop a crust.
It will actually improve flavor-wise for a couple of days in the fridge. Since it's a flat bread you don't have to worry about over-proofing, either.
It should be fine in the 'fridge a couple of days. In fact that's recommended.
I find it can dry out in a bowl in the fridge and plastic wrap always tends to get shifted somehow and give me a dry spot.
My space saving tip is use those free large plastic bags you find on rolls in the produce section and give them a spray with oil and put the ball in that, leaving a little room for expansion.
I'll sometimes ask the cashier for what is basically the same size bag they use at check out for wrapping meat products before they bag them. They usually end up giving me a dozen or so when I tell them it's for poofing bread doughs.
I divide the dough with a bench knife, ball up two or more pieces and wrap it tightly in cling wrap. Per the above comments it really does refrigerate well. And it freezes well too.