The Axis cameras are very good. I have used Axis cameras for quite a few years. The wireless will work fine, given the limitations of 802.11b. All the Axis cameras that I have used run of mains power. They have a little plug in wall transformer. I suppose you could make them run off a battery too but it would be a pain to change out that battery every so often.
The next generation of wireless devices will run off what's called "power over ethernet". However you would have to have a "power over ethernet" switch to run them. They do not need a wall plug. They are powered over the Cat5 cable.
-Target