Marena was wondering about Snapfish for her photos. Leo says that's more geared toward people that want to pay for prints, and he likes Google's Picasa Web. It's free, and will automatically upload all of her photos to Google. She can also buy more storage if she needs more than the 7GB Google offers free. If she wants a more professional service, Leo uses and likes SmugMug as well.
It's important to have a backup, so this would take care of having one off-site. Leo also recommends getting an inexpensive USB external storage drive to put her photos on as well.
Carbonite is another way to keep an off-site backup of everything, but in this particular case it may not be the best option since Picasa is designed for managing photos. (Disclaimer: Carbonite is a sponsor).