Hi Tobiasrer, welcome!
On UP milk, our
Wiki: Milk Processing gives some info. As Mrs KK says not all milk or cream is labelled UP, and definitions of UP are different depending where you are in the world. Here where I am in Houston USA, most retail Organic Milk, Half & Half, Cream, and Goats Milk is UP. Basically it is almost biologically dead and hard to get a good rennet curd set with. Here's a
good thread on UP. The highest pasteurization is UHT, here's a
good thread where linuxboy says that UHT and thus UP is good for making Lactic coagulated type cheeses.
Pasteurization hurts rennet coagulation of milk, to compensate your add CaCl2, see our Wiki: Calcium Chloride.
I've only ever used store bought pasteurized milk, as do many others here, no problem (although some have reported problems with US Wal-Mart milk.
Moz and Cheddar are not easy starter cheeses, theres a Wiki article for New Cheese Makers that has some good ideas.
Have fun!