For the absolute lowest cost, that would be the Mac Mini. If you have an existing display it is the cheapest way to go.
If you have to start purchasing a keyboard, monitor, and mouse, then you are getting closer to the $1,099 macbook. Probably not as much, but pretty close.
You are also getting close to the cost for the Refurb iMac's. Remember that the refurb products come with the same Apple warranty as the new ones. For all practical purposes, they are as good as new.
All of the current machines run Leopard and come with iLife (which includes iPhoto) for basic photo editing.
If you are just getting started, and don't have much cash, the Mini is a good way to go. If you can afford a little more, then get a MacBook, or an iMac (new or refurb).