I use a couple of milk-crate-style storage containers to keep a large assortment of moldings and dowels organized. The crates usually measure about 12" on all sides, and have a grid on the bottom. Start by screwing two of them together, one on top of the other. Then turn them upside-down and attach them to a piece of plywood sized to fit the opening (which is now on the bottom). The resulting storage unit is light and inexpensive, and the two grids keep thin stock organized.
There are several variations you could use: Keep the crates in the intended open-end-up position, and use the open part for storage of short pieces and still use the grid for long, thin stock. You can add wheels for portability. You can even use it to store long-handled tools for the shop and garden.