When on wifi, the photo backup upload starts immediately. If it doesn't (possibly due to your settings, this used to be my issue) you can manually open the photos app and tap the backup now button.
Google Drive would be another option to transfer, but would be more work (about same to "share" as email, but less convenient to access on desktop).
The e-mail way is actually quite convenient since on the desktop you can just download all the photos you sent in one go - they appear as a zip file that you can then just extract to your working directory, rather than having to save one at a time.