I keep my assortment of screws in one of these https://www.grainger.com/Grainger/FLAMBEAU-Item-Adjustable-Compartment-Box-1NTH5?Pid=search
But some of the part I have are too small. They can slide under the plastic dividers. I printed some small bin that slide down inside the dividers to hold the small parts.
They came out great. If you want to print some too you can find it here: http://www.thingiverse.com/thing:165313