Just a note that the backs for the model I and II have a lithium battery that is soldered in. These batteries were not intended to be user replaceable, and most of them will have run out of juice long ago. Those backs will also work on a model III, so don't assume that a model III body will come with a model III back. The model III backs have a compartment for easy installation of standard lithium batteries. Unfortunately, the lithium batteries that are used in the model III backs are different from the ones in the model III body, so you need to keep two types of batteries on hand.
If you have a model I or II back with the soldered in battery, you can disassemble the back to install a replacement. The replacement is a 1/2 AA lithium battery. If I remember correctly it's either 3V or 3.6V. It's a pain in the butt to swap it out, but at least it's doable if you have some technical ability. These backs are often very cheap, since the batteries are usually dead. You can probably still use the back if the internal battery is dead, since it will draw power from the camera body to advance the film. The downside is that if you remove the back from the camera there is no power to store the frame count, so the camera won't know what frame you're on the next time you install the back.
Familiarize yourself with the appearance of the model III back, and how it differs from the model I/II back. Lots of sellers don't know the difference, and may throw the older model back on a model III camera. The model III backs always go for a lot more money, due to the easily replaceable battery, and will work on all versions of the camera body.