I'm going to answer your post from the perspective of you being a relative beginner in electronics / programming (that seems to be what your post implies), but I don't mean this as an insult - we all start somewhere!
First off, the hardware side of things. You'll need a device as your base that's fast enough to handle the tasks you give it. Video playback is possibly the most strenuous, and that in itself demands an ARM based processor (forget your traditional 8 bit micros, just not powerful enough. Arduino can go out the Window as well.) This brings up a few issues on the hardware side of things, since ARM chips generally don't come in thu-hole design (please, if I'm wrong someone point me to one that does!) so you'll need to be rather handy with a soldering iron, or get yourself a dedicated ARM development kit. This is before you start trying to interface it with other devices such as cameras, an external display and so on. When you do get past that, you definitely won't be able to use Python either.
It's possible, but as a beginner it is not a place you want to start.
If you're still dead set on doing this, I'd base it around a Raspberry Pi. It won't be the most efficient way of what you want to do - but it gives you a Linux environment running on minimal hardware with HDMI out (which can be used to interface to a screen to playback video) and you could atttach a camera via USB or GPIO. You could also use Python on top of Linux to do what you want.
Cost? Really does depend on components, but I'd be surprised if you can make something like this in this fashion for anywhere near the price of say a ~£100 phone that can handle these functions. In short, interesting project but I really don't think it's worth the time or expense.