Everyone has suggested most of what I bring with me except for a tool called the purple thangy (a plastic stilleto-type tool for guiding fabric and such).
I use a kniiting bag that's about 10" deep x 12" high x 15" wide; it has lots of pockets and zips across the top. Home improvement stores (Home Depot, etc.) also carry all sorts & sizes of canvas tool bags. I found a plastic container (the size of a small flat cake container)that fits nicely into it, on edge. All my fabric for the project/class or WIP fits into it. I also carry the jumbo size zip lock bags, and a couple of sandwich size, to group/store things together.
Lastly, because I'm not a coffee drinker, I always have diet Pepsi cans with me, transporting them in my work bag. Do you know how EASY it is to puncture one of these cans with a ruler (point)??? Yup, on two separate ocassions, I've punctured a can without knowing it, only to find a puddle at the bottom of the bag when I get to class!! :-( First time wasn't tooooo bad but, the second time, I ruined a nice chunk of fabric! Thankfully, the shop still had some in stock.
My solution to this was to buy some insulation batting (at Joann's) that is used in lunch bags, plus a scrap of decorator fabric, to make a cylindrical tube, closed at one end, drawstring on the top, to transport a couple of cans. I figure this should be heavy duty enough to thwart (don't you just love that word... thwart) the sharpest of rulers. Ta da!! :-)