The cheapest digital point-n-shoot will do what you need, but I would spend the extra money and at least get a name brand (Nikon, etc..) Photography is a hobby of mine (*some would say sickness), and my point-n-shoot is a Nikon S-550. Really powerful camera for the money.
If the $150 price tag (new) scares you, you can probably get one (or similar) on Ebay, pawn shops, etc...
But really, if your primary focus (no pun intended) is security / surveilance: Look at the GoPro camera. You can wear this baby on your head, like a miner's light. It will record continuous HD-video to an SD memory card, or even time- lapse photography (every 2, 5, 10, etc.. seconds) at 5 megapixels.
For that matter, a cheap GoPro camera can even be set up to default as a camera. (not video) That would also fit your bill, and they are really pretty small. (if you remove the polycarbonate, waterproof housing). Link: