I understand how to sync photos to my iPhone but they seem to be placed on the phone in a rather random order. I've tried numerous changes to the photos but they don't appear to be organized by date, size, or alphabetically by name. Am I missing something?
They are sorted in order of EXIF creation date, which is not necessarily the same as the Date Created shown by the finder.
You can use
exiftool to view and also set these dates to sort your images...
exiftool -overwrite_original_in_place -CreateDate="2008:12:18 12:34:56.78" MyImage.JPG
When you sync with iTunes, sync them into a specific folder and always use this folder. and Don't change their order and select in iTunes Sync Photos.