I'm on vacation so I can't check what we use, but I can tell you that using regular AA/AAA batteries is a good thing. For our cameras, we have small Pelican cases for the camera and a spare set of batteries, which really helps with bouncing around in the car. Invariably, when I go to get the camera out, the batteries are dead, so it is simple to pop out the old ones, pop in new ones and go. If they used a rechargeable battery, it would never be charged, plain and simple. We have had a few problems with people using the replacement batteries and not replacing them, but not a lot. Myself, my pocket carry flashlight is AA and our cameras use AA, so I keep a few spares in my duty bag so I have them in case I need them. It is just so much simpler and easier using AA/AAA batteries than it is rechargeable battery packs.
As for the cameras themselves, not really sure it matters for point-and-shoot cameras. In fact, given that cops can fuck up anything, I'm not real sure that it matters if you buy really good ones or not. I do know that the Cpl who takes care of our pics and cameras bought ours from Amazon. Just buy easy to use cameras and you should be relatively good to go.
Bub