Re: raspberry pi
Certainly, you can do things like that - and if you want to tinker, then it's a great way to start learning about how everything works. But cheapness isn't always everything - and with the Pi by the time you've added a camera-style case, and perhaps bought a HomePlug to connect it to, you're actually not that far off the cost of something like this (Pi is a little under £30, camera module just under £20, add a PSU, case, etc).
Of course, you can do a hell of a lot more with a Pi, and it would be interesting to use one with, say, USB webcams, or other IP cameras, to aggregate several images, which something like this can't do.
But, on the other hand, if one camera is enough, and you just want something to plug in and start using, then solutions like the ones mentioned here will solve a problem. A lot comes down to the trade-off of how you value your time, and where you're using it.
Home brew might be fine for your personal use, for example, but if I were installing something in my mother's home, 80 miles away, the benefits of having just one cable to plug in and nothing else that can come loose/crash/be tinkered with outweigh the fun of DIY