What is the appropriate name for camera modules/sensors? And what kind of supporting circuirty is needed?
You have got the nomenclature correct.  A module contains an imager and lens and focussing element.  Most of these imagers operate over an I^2C bus for control and a MIPI bus for the data flow.  If your controller supports those interfaces it will be as simple as just connecting them.  There are imagers that use other interfaces (Parallel , Analog) but these are not used in modules so I won't mention them here.

Your big issue is going to be understanding how to operate the device and what to turn on/off in the registers.  This is not commonly published and is typically only disclosed under NDA (Non disclosure Agreement) and NDA's are typically not signed unless you are a going concern and will drive volume.  Your best bet is to find an OS that has explicit support for the camera module you are going to use as the support will be "baked in".

The other option is to use a imager set that doesn't require an NDA and the information is published.  Like an ILD CCD, a board camera (typically used in security applications) or similar.  Perhaps you can get a complete USB camera.