You are correct about the [File] tags, they are info about the file from the underlying filesystem. Create Date/Time is the timestamp for when the file was created. I believe that File Modification Date/Time is changed whenever the the file is opened for a write operation, even when the write is 0 bytes. One of its main uses is to let backup software know that the file has been changed. Under Windows XP, File Access Date/Time was changed whenever the file was read or written to. Later versions of Windows had this turned off by default, but it can be turned back on with a reg edit. I think there are some differences if you're using a Mac or Linux system.

Composite tags are not tags that are actually part of the file. They're created by ExifTool by combining other tags that are in the file. In your example case, they are directly copied from the EXIF tags. But there can be cases where, for example, Date/Time Original doesn't exist in the file, but there may be a DateCreated and a TimeCreated tag. ExifTool would combine these two to create Date/Time Original. This would be unlikely for a modern camera picture, as they usually save such info in the EXIF block. See Composite Tags for more info.

That leaves the EXIF tags. Date/Time Original and Create Date should be the same for a modern camera picture. But if you were, for example, scanning old pictures, slides, or negatives, the Create Date should be the date/time you saved it to the file and then you would alter the Date/Time Original to the correct time, if you knew it. Obviously, few people are going to know the exact time a picture was taken and probably not going to bother.

Modify Date would be the timestamp for when you might alter the image or it's metadata. This is a tag that hopefully would be software controlled, by Lightroom, for example.

IMO, the best tag for sorting would be the Date/Time Original tag. In most circumstances, you could just use DateTimeOriginal in ExifTool, though if you want to be specific, you can use EXIF:DateTimeOriginal. Odds are it'll be same timestamp either way.