One of the most important factors, in my experience, for achieving a round pizza is to begin with a round dough ball. This means either proofing the dough ball on a flat surface (like a tray) or using a round container, not a square one.
One of the videos you've been watching is this one, right?
Don't worry about tossing. Some people will say it dries out the skin, but I don't buy into that.