It's hard to imagine a pizza without mozzarella. This wonderful traditional Italian cheese is now made all over the world. It has a fairly short shelf-life and really is best consumed when it's fresh. And you can't get fresher than home-made.
A note about milk: ultra-pasteurised (UHT) milk will not work. Ideally, you would use raw, unpasteurised milk, but this is very hard to obtain. I use non-homogenised milk, and that works fine.