Small DVR with integrated PoE - where to find/what to buy?

Have you tried breaking down the steps? Something like

1. Mount camera in required position. Refer to mounting instructions.
2. Run CAT5e/6 from camera to DVR. Ensure both ends of the cable terminate by T568A color standards (or use a premade factory cable)
3. Connect cable to camera. Connect other end to DVR port 1.
4. Repeat for all cameras.
5. Turn DVR on and wait (as per instructions).

Those are very simplified instructions, but they'll get an electrician working. They are also by no means Best Practices either, but hey, that's why you're using an electrician and not a low-voltage tech, right? ;)