Yes you can ignore iPhoto and upload directly to Picasa/Google Photos (web address https://picasaweb.google.com/home) but this does not RESIZE the images, so you will eat up your storage limit very quickly... Fine for students, not so much for teachers.
Short and simple - the best way to do this is using iPhoto with the Picasa Web Album uploader, here, which bypasses iPhoto, and lets you drag and drop images for upload, all resizing options are available as above.
- Import the images to iPhoto (drag and drop on the icon on the dock)
- Remove the photos that you don't want
- Select the photos you want to share (select individual images, a whole album, or event)
- Drag and drop to the uploader
- Choose 'Unlisted Album' (this is automatically 'anyone with the link' in Picasa = perfect for our purposes)
- Choose 'Faster Upload'
- Click Export
- When it's done, you'll get a 'View' option, click that
- Share the album via the Share button.
- Click the box "Let people I share with contribute photos" if you want that option, they will need a Google account to be able to contribute, comment or like images in your album.
Easily confused: Picasa Web Albums vs Picasa the application:
Images can can only be downloaded one by one from a Picasa album, unless you download and install Picasa the application (free) which basically does the same job as iPhoto (image management and editing) but will also allow you some other options, like downloading entire albums, and syncing your albums with Picasa (as opposed to just uploading to Picasa).
Your parents cannot download video, or an entire album from a Picasa web album, only view, unless they 'upgrade' to Google+ then they can. If you wish to share video that you want the recipients to be able to download, (without using Google+) then share it via Google Drive.