I've tried a number of different approaches, but prefer the longer method using thermophillic starter, rennet, and lipase. I think I can taste the difference on the final pizza, but you can especially taste the difference when eating it fresh, something I always do when I make a batch (fresh tomatoes, basil, mozzarella, EVOO, salt, pepper - mmmmmmmmmmm).
It can take less than a day to make. While stretching, I try to squeeze out as much moisture as possible so I don't have a puddling problem when baking. I do bake my pies at very high temps and I think this helps. Contrary to some instructions, I prefer to use freshly made cheese - it has a sweeter flavor.
The recipe I use is from "Home Cheese Making" by Ricki Carroll and I use unhomgenized milk. When I started making this cheese, I was pretty obsessive about checking pH along the way. I've gotten lazy through the years and now go pretty much by instinct. But if you are just starting out, owning a a pH tester is a good idea.