be sure to label ALL of your tools, rulers, scissors, rotory cutter ect...when a dozen people all have the same brands (stuff) can happen. i use masking tape...or a sharpie and write right on the tool.
it depends on the class what to carry stuff in...i carry a sewing box if i need lots of different tools and notions...if i don't need that much (stuff) i use a tote bag. call the shop and ask if you need your own cutting mat or if they will provide one for every one to use...also check on iron- machine, ect...
our shops give us a supply list when we sign up for a class telling if we need mats, irons, machines, light boxes, ect...sometimes most of this is available, some times it is not. you don't want to haul a bunch of stuff you do not need.