Definitely keep the materials in their original bags after you cut off the material you need. You'll be amazed how many different materials you need and how easy it is to confuse them, plus they'll get damaged if they're not in bags.
I simply keep mine in the bottom of a large plastic tool box, and use the tray in the top to store the tools and smaller items like hooks. I'm a pretty rookie tyer and I don't have a ton of stuff though, so I don't need a ton of space!
My passion for catching fish is eclipsed only by the fish's passion not to be caught.