[COLOR=DarkOrchid][SIZE=3][FONT=Comic Sans MS]To get the spiral effect, start your tube with a couple rounds of plain knitting (see below). Then at the beginning of the round, K1, P2, Knit around. Next round K2 P2 Knit around. Next round K3 P2 Knit around. Continue in this manner, moving the P2 sts around the tube. If you want a "lip" on the end of the tube, do a couple of P rounds before binding off.
The rule of thumb I've been using is to make an object to be fulled about one third longer than you want the final project. Items generally full more in length than in width. The size of an item is totally dependent on how long you full the item. I generally check every 5 to 10 minutes and take it out when it's the size I want. I also use white vinegar instead of soap so I don't have to worry about the item fulling even further during the rinsing stage. If you have a long tube like a piece of PVC pipe or something you can slip the wet tube over it to help it dry nice and round. Or stuff with grocery bags to help it block nicely while drying. Or maybe even the knitting needles (not wood or bamboo) you want it as a case for.
As I don't like starting with one stitch and increasing, I'd cast on with waste yarn and do a couple rounds with that. Then start with the good yarn. Once you've bound off, take out the waste yarn, run a needle with yarn through the live sts of the tube and gather. Secure the end.