Came up with two possible designs:

1) Raspberry Pi approach:

• Raspberry Pi Zero - $5
• Simple WebCam - $2-10 (could use old donated ones too)
• PIR sensor - $1.5
• Micro SD card (4gb probably enough) - $2-3 ?
• Battery
• Case
• Optional IR lights

Pros:
+ can connect to any WebCam (or any additional tools if necessary) via USB
+ can be connected straight to a monitor for analysis later
+ would not consume too much battery power
+ can be programmed to stand by (save energy) when there is no action, and woken up again to take the picture
+ easier to reproduce and build yourself

+ can program anything on Linux

Cons:
- difficult to get Raspberry Pi Zero
- would take time to program on Linux

2) KeyChain Camera approach:

• KeyChain Spy Camera - $5
• Arduino that controls the PIR and Camera - $2
• PIR sensor - $1.5
• micro SD card (4gb probably enough) - $2-3
• Extra battery
• Case
• Optional IR lights

Pros:

+ cheap parts

+ easier to get the parts

+ there are also better KeyChains with motion detection

+ easier to program

+ uses less battery life

Cons:

- would need to install a bigger battery

- requires soldering

- photo resolution not so great