I have a whole bunch of Stack-On brand multi-drawers in my shop to hold everything.
The question for you will be "will you be moving any time again after your move" - for me it was "no, not for more than 10-20 years", most likely; so the multi-drawer boxes made the most sense.
If you think you will be moving, or you want a more portable way to move your parts, think about something like fishing tackle boxes. They make several different kinds, many with clear inspection windows. Some are designed to be easily stacked. You might even be able to find some that can be stacked and used on a bench like regular multi-drawer boxes, but portable.
There's also specialized tool boxes and such with dividers and drawers and similar partitions available for electronics and regular hardware (go to your big box home depot type retailer and look), that might be able to be used - meant to carry parts like screws, nuts, bolts and such on job sites (home construction and such). They may or may not be more or less expensive than fishing tackle boxes.
But here's the key - whatever system you ultimately use:
- Buy more of the boxes than you need (because, eventually, you'll need or want more).
- Buy and use a label maker for labeling your parts bins.
The reason for number 1 (and this applies to any time you are buying storage containers of any sort) is that inevitably, you'll run out of space in the containers you have, and want more. You'll go to the store - and find that the container/case you bought before, is no longer made or sold (not really true for Stack-On brand multi-drawers - that's one reason why I like them - long-term availability); having all kinds of different style containers/drawers/cases/toolboxes makes for a storage nightmare. So invest early, and invest a lot. It won't be cheap, but it will be worth it long term.
The reason for number 2 is so you can easily identify and find your parts; you want to sort them and store them in logical groupings, so many of each type in each bin, with bins arranged in groups (so you might have a tackle box or multi-drawer of only resistors, and another for capacitors, and yet another for something else, etc). Also - always leave a few empty bins available in each case/container/etc - so you can easily expand (that's something that's nice about multi-drawer boxes, though - to expand, you just place and shift the drawers about - other solutions may mean you have to move parts, because the drawers/bins/whatever aren't removable - which can be a pain).
Whatever the system - it needs to -be- a system, and not just a mishmash jumble. Plan the system out beforehand - how you want it to look, how you want to arrange things, what kind of parts (and how many of each) you plan to have on hand, what the logical groupings will be. Once you know that, then you'll have an idea of how many bins/cases/etc to purchase, plus how many extra for future expansion.
Also - take a look around at your options, and try to choose the option that, should you need more in the future, you likely can get the same one (as I said, Stack-On has been pretty good in this regard). You might find something else. You might find that something "homebrew" works really well (baby food jars with the lids nailed/screwed to a board, for instance) - where the containers haven't changed much in decades. The ultimate keys here are consistency, labeling, and logical placement for storage.
Lastly - realize that doing it this way above will not be cheap - plan on spending a couple hundred dollars or so on storage. It will ultimately be worth it. I did this process last year, around this time - to my own shop. My storage solutions that I had in place was completely broken down and no longer serving a good purpose. I ended up spending quite a bit of money upgrading my storage (not just small parts either - I bought a few gorrila racks for shelving too) in my shop, and now I couldn't be happier (ok, I wish I had a larger shop - see the problem?)...
;D
though that is a bit personal
Love film!