I don't know what your budget is like, but one option that I think would potentially work very well, and have a good "wow factor", though I'm sure would be expensive, would be a custom solution from the likes of Perceptive Pixel. Their large multi-touch displays could surely be a great way for your customers to find photos of themselves (and/or their friends), and perhaps even place an order through the interface, to be confirmed and finalized by your staff member.
Another option, too, though I don't know if it's readily extant/available, would be to have software that does face detection to match (via a webcam or similar) the person walking up to the kiosk with the database of the images you recorded. Getting false positives or negatives would potentially be a concern, here, but it sure has the potential to make things quick -- and face detection has been advancing greatly in recent years. I imagine the Perceptive Pixel folks might be up for implementing such a solution, too.
If you're not familiar with Perceptive Pixel, one good introduction would be the talk Jeff Han (founder) gave at TED in 2006. It's an interesting talk, with some interesting ideas about the future of user interfaces. If he's the kind of person you'd want doing your kiosk, then Perceptive Pixel is surely the way to go.
Note: I am in no way associated with Perceptive Pixel -- I don't work there, I'm not a customer, I don't own stock -- I just have followed them somewhat since first running across the TED talk listed above, and thought of their solutions as being a good fit for what you're describing -- provided you can afford it, at any rate. :)