With store bought milk, you may be able to make an acceptable mozz with a citric acid recipe. I started this thread
which includes the recipe that I developed, making tweaks to another recipe that gave me some mild success.
If you want to try a cultured recipe, you can substitute 1/3 cup of plain, active culture yogurt for each gallon of milk. Using pasteurized, homogenized milk you should probably use calcium chloride as well, to get a better curd set and higher yield.
You did pick a tough one to start on, but most people are attracted to it because it doesn't require special equipment or a place to age the cheese. It can be done, though!