When my wife started doing video editing a while ago, I got her a desktop computer with a large harddrive, and I signed her up for the $5/mo Mozy plan. It's a pretty reasonable price, and we've already restored a couple videos she somehow managed to delete accidentally.
You don't need a powerful computer for photos, but it sounds like you do need more disk space. If you don't want to replace your laptop HD, you could get a large external USB HD.
Something else that I do, since I am the one that manages the photos (as opposed to the videos) is I put the photos on my computer and manage them with Picasa. I upload all the latest at a reduced resolution to Picasa Web Albums to share with family, deleting older albums when I get close to the 1GB limit (who wants a lifetime of photos to be public anyway?). And I occasionally sync all my photos over to my wife's computer, so that they get backed up to Mozy too.