The Pi is a much better technical fit for the project you outlined. The Pi will be a bit more expensive but I would have thought the Arduino would be roughly 2/3 of the price so not that great a difference. Plus the Pi has a lot of built in facilities that you may need to add on to the Arduino e.g. ethernet, wireless, hdmi . You might want to think again about this if it is not already set in stone.
Maybe you should post more of the project description that you gave the panel.
What are the timescales?
The Arduino is great for control but not for image processing.
Get a PIR that does detects movement and gives you a contact closure.
Get a camera that can be operated by the Arduino, it sounds like you need it to be able to take both stills and video.
Here is a list of cameras (there may be other better ones) 10 Best Arduino Cameras
The Arduino can monitor the PIR. Once the PIR detects movement the Arduino can send an email. You will probably want a wireless or ethernet shield for this. The Arduino also needs to then operate the camera to take stills and video. The Arduino has very limited memory. Images could be stored to an SD card or streamed straight back to another device, probably a PC.
The image handling would be a lot simpler with a Pi because a PC user could use the wireless connection built into the Pi and VNCViewer to see" what the Pi camera can see.
So your project is probably possible but there is a lot to learn. Start doing very simple programs on the Arduino ASAP and work through the examples to build up to your project.