I have tried many different options over the years. I currently use lidded boxes made by Sterilite. Each box measures 11"L x 6 5/8"W x 5 3/8"H. I sort the charm squares by hue and value. My preference is to store the squares vertically in each box so that I can choose what I need by value (I'm an art quilter). I bought the boxes at Big Lots and they cost $3.50 each.
FYI: I've used the ArtBin Satchel and Super Satchel in the past for storing charm squares, but find the smaller Sterilite boxes easier to handle.
Hope you find a solution that works for you...