whichwhey, good question, I assume you mean cow's milk.
So far I've made 50 batches of cheese and
all with store bought
milk. Mostly past & homogenized whole cow's milk and no problem, one with 2% also no problem, one using Ultra Pasteurized (ie almost dead) goat's milk, I did not get a good curd set.
Stay away from UP milk, run away from UHT milk and as you say, search through shelf to find freshest date. Also, I always buy the cheapest stuff on sale which here in Houston Texas is USD2 per US gallon
.
Have fun!