I prefer these storage bins made by Stanley. They are fairly inexpensive and the small bins are removable so that you can easily grab the whole bin of screws or whatever. This also makes them easy to re-arrange your small parts. If you look around you can find them in two sizes — a thick and thin version.
https://www.homedepot.com/p/Stanley-25-Compartment-Shallow-P...
Also, a cabinet for storing the organizers is an easy build for a new woodworker: