I have one that I seldom use anymore, so my experience is somewhat dated.
They make trail cameras that send images to your phone in real time, so i theory at least the card is secondary. They make SD cards a lot bigger than 16GB and they are cheap, so be sure the camera you choose can take a bigger card to alleviate that issue.
My shooting club is using the Cell service cameras with success.
Whether or not 16GB will be enough will depend on the format the pictures are stored in, and how often the camera is triggered. I think the battery life will be the limiting factor though, as even the most energy efficient of monitoring is going to cause some constant power drain.
You can buy some pretty big aux battery packs. You can also buy solar-powered USB chargers. OP would want an aux battery and/or charger that are weather-resistant.
Typically they use a PIR sensor to detect movement and trigger the video recording; this is the same sort of sensor as used in intruder alarm systems and typically it’s only triggered by a moving object which is at a different temperature to the objects in the background. Some trail cams have adjustable PIR sensitivity.