You can set your photos to public or private, and you can also copyright them on Flickr. I've found it to be very safe and efficient to upload. You can them set your privacy controls to allow your friends and family to share/see the pictures. I've done this with our heritage photos. I scanned them, uploaded, had my family get their own (free) accounts, and then allowed my family to see the pictures. They can then also add information to the pictures in the captions, which is helpful when doing family history. I'm very happy with Flickr.
If you're going to add lots of photos, though, you'll need a pro account pretty quickly. I have thousands, and I'll keep my pro account to enable access to them.
As for my backups, I do need an off-site backup, too. I just haven't gotten around to it, which I should know better, as I've had a hard drive loss!