You can get good quality flash type cameras- like the wildgame - which I got for $65 including shipping (free).
If you are putting the camera out in a place the flash will bring in thieves - well go infrared.
I put my wildgame out on a trail that I had taken a deer last year. I went to find it at midnight as it is so close to a bedding area.
The camera was gone.
But- I had seen overturned rocks and bear scat; and walked around until the cameras flash led me to the camera.
I know there is a 50/50 chance it landed with the flash pointing up- but it was pushed into a boggy area that it may not have survived over a long time- and I did find it.
Note to fellow idiots: the memory cards have a lock on the side of them- if the lock is in place- well... your not going to get any pictures. I didn't even know it was there until the trail camera had zero pictures in it...