Sue, while I don't have alcohol markers, I do have 2 other types of markers...and prismas...and watercolor pencils...and watercolor crayons...and I'm planning to add inktense to that collection.
So, I do have to stay organized or I'd go crazy! I have several pencil storage units that I "scavenged" from a local art store that hold all my coloring tools. I have mine in those bins first by media type then by color. To apply that to your situation, I would have those markers grouped by color group first and each bin would hold a couple of color groups...arranged by hue (color).
So the bins would look something like these:
Here's an interesting storage that puts the color groupings in individual bins:
But I have seen other ideas that are meant to be portable:
And then there's the "official" copic storage:
There's a gazillion ideas online if you google "copic storage".
PLUS, here's a search on Pinterest...some great ideas there too.
Here's a neat idea:
not storage, but great organizational idea!