It took me a long time to get the hang of the mandoline for cheese. I really like it for veggies though. Try it for the veggies for the pizza. For the cheese, I'd either use the rotary grater or coarse microplane if you have either. If not... either keep practicing or go w/ the preshredded.
If it helps to know I've only been using it for cheese for the past 6 months and I've had it for 3 years What I do is take the cheese straight out of the fridge, and I rotate the chunk whenever it starts to tear up... (I also don't use the guard, but that's not EVER something you want to demo.!!)