Once the plates are dry, it doesn't matter whether in which orientation they are stored. As long as they cannot rattle around. 14x20" is pretty big; breaks easily.
For transportation of still-wet plates vertical would be nice...but I doubt it's really necessary to consider this use-case since collodion plates dry quickly anyway. So I'd just wait until they're dry before boxing them up.
A box might be nice, but is not strictly necessary. You could also fold the plates into a suitable packaging material (e.g. a suitable kind of foam) together with a rigid support (e.g. two pieces of plywood).