Sandpaper storage is a frustration - Preacherjon has a solution, but it requires three boxes to hold his full range of grits. I don't think that would work for me since I like to keep my sandpaper on a small rack that sits on the floor next to my lathe, and three boxes wouldn't fit on the rack without the risk of falling off.
Instead, I use a box (also from Harbor Freight) that has seven full size compartments, and a couple of smaller compartments at the ends. I stock 100, 150, 220, 320, 400, 600, 800 and 1200 discs. The compartments are large enough to accommodate 2 3/8" discs from front to back, but not from side to side, so the discs have to sit on edge.
The ideal box for me would have eight compartments each 2 1/2" square so discs could sit flat. I haven't found it yet, but I'm still looking!
Conventional wisdom is to never skip grits, but there was an article in Woodturning Design about 10 years ago that was sort of an 'everything you wanted to know about sandpaper but were afraid to ask'. The author of that article repeated the 'don't skip a grit' mantra, but then noted it was arbitrary and that the key point was not not skip so many grits that it became difficult to remove the scratches from the earlier grits. Instead, he suggested not advancing by more than 150% in grit rating in a single step.
By the way, when I first started turning about 10 years ago, I bought one of the 'Turner's Bargain Boxes' from Klingspor. These are large boxes that contain a selection of grits typically used by turners - the abrasives are all cloth-backed rolls and are remnants left over from the process of packaging abrasive rolls for industrial use. Mine include both very heavy (stiff) abrasives as well as some very flexible cloth-backed stuff, and included 180, 220, 240, 320, 500, and 800 grit material - note that with the exception of the 240, this sequence also essentially follows the 150% step rule. That box contained a lot of abrasive, and I've only used about half of it - it truly was a great bargain!