I rather advise RaspPi because this sort of MCU need support from community. Without community supports, you can get frustrations and end up dumping aside after wasted your months of time.
Fashim, everything is expensive and your time is also money. If you do not make this project, you save more money. The least cost is depends on what is your requirement. A simple low resolution camera taking a shot is much easier. Check around internet, there are few projects there. You have to do your homework before asking. That way you save your time more.