The arduino could be setup to operate a camera and monitor a PIR sensor which would tell it when to snap a picture. It hasn't got the horse power to send that data over the internet without an expensive module. It can do bluetooth but that's even more expensive.
I think you're looking for a single board computer, something that can run UC linux and would be able to operate a usb web cam. Then all you'd need would be GSPY
Or better
Single board computers that run linux. IMHO avoid the jackasses that won't give you a price online.