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Carrying cases range from the tough, hard-sided cases (e.g. Tudor. Orion, Pelican), to soft-sided cases (e.g. Warhammer, Feldherr), to basic plastic trays. The foam insert trays are expensive, but they are very light and provide great protection.
Here is a video of some storage options (note the dramatic opening scenes with no sound... powerful!)
[embedyt]https://youtu.be/Tj3Eau2iktM[/embedyt]
The Feldherr case with foam inserts is a great storage option.
This Tudor Team Case is more compact, and it holds 22 figures.
I have a very similar case to the Orion. The "pluck-out" foam squares are about .5in x .5in x 2in. Two plucked squares is a nice, snug fit for a player, so you can see the optimal pattern in the video. I wound up with 98 spots (7 rows with 14 players per row.) The case is nice, but I prefer the five foam trays in my Feldherr case.
There are many varieties of plastic parts organizers. The Plano brand is inexpensive, but their quality is very good. I use these cases for all sorts of small parts (not just EF stuff.)