I think you will find that it can be done either way but how you intend to use the dough may be a factor. For example, in the professional ranks, some pizza operators will make the dough in bulk and ferment it in a tub or large bag at room temperature, usually (but not always) for same-day use (the dough will usually be held overnight in the cooler for next-day use or used as scrap to make the next-day's dough). Often the dough pieces are run through a roller or press so the shape of the dough cut out from the bulk is not especially critical. Similarly, if the dough is to be pressed into a pan and then allowed to proof (rise) before dressing and baking, the shape again will usually not be a particularly critical factor. For cold-fermented doughs intended to be hand shaped and stretched into skins, the more common approach used by professionals is to divide the prepared dough into the desired number of dough balls--doing this by hand or by using a divider/rounder if the volume is high enough--and place the dough balls into dough boxes or trays and then into the cooler. This approach reasonably guarantees that the dough balls will cool down faster than a bulk dough (because of their smaller size) and retain a nice round (albeit possibly flattened) shape when ready to use, ensuring minimal loss of gases in the dough because of overhandling. From what I have read on the forum on this topic, I believe most of our members who make cold fermented dough balls use the individual dough ball approach rather than the bulk approach.
As far as how much counter time should be used before making the pizzas, you can use either temperature or time as the guide. Generally, if you try to shape a dough ball that has an internal temperature below, say, 50-55 degrees F, there is an increased chance that the finished crust will have a lot of big bubbles. The likelihood of these bubbles occurring can be reduced by docking the skin heavily with a dough docker before dressing and baking, but some bubbles may still appear in the finished crust. Some people actually like big bubbles in their crust, so it is a personal matter to some degree. But, professionals hate bubbles. The more common approach (rather than taking the temperature of the dough) is to allow about 1 1/2 to 2 hours counter time before shaping the dough balls into skins. The actual time will depend on the dough temperature coming out of the cooler/refrigerator and the room temperature. Usually a dough will rise much faster in the summer than in the winter. It isn't critical that you stay within the 1 1/2-2 hour time period mentioned above. In most cases, the dough will be usable for about 3-4 hours or more after that.