fresh pasta newbie
No -- most fresh pasta recipes can also be dried. I think the thing about fresh pasta that makes it special is the fact that you can make the pasta thin and thus more tender than store-bought brands. I find that it's best if you use it for ravioli or wide fettuccini, personally.
I definitely wouldn't "bag it" in a plastic bag when coming home from your class. Rather, if they are the long/thin type, I'd make them into a nest and store in a paper bag. Freshly made pasta isn't special because it's soft when you put it into the boiling water -- it's special because of the ingredients and the texture, which is not spoiled by drying a bit.
The first time I made pasta was at a cooking class. They had us put it in ziplocks to take it home. I stopped at the grocery store on the way home, so I didn't get mine home immediately. I put some in the freezer and some in the fridge when I got home. I cooked the fridge stuff first (obviously) and the frozen stuff days later. Neither seemed to be affected by the trip.
My advice though is when you store it, separate it better than I did until they are dry. The thin noodles I made ended up clumped together and didn't separate during cooking. I assume they weren't try enough when I put them in the ziplocks.