In the $100 range many of the Wildgame Innovations or the Moultrie D55IR would work if the only thing you are intersted in is an inventory. I will say that the quality on any cheap camera is hit and miss. You might get a good one or you might not. If you have to replace a cheap cam two or three times then it is no longer cheap. If I were you I would go with something in the $150-$200 range. That would give you many more options. And while not guaranteeing you will get a a camera that won't ever give you problems, it will at least give you better odds.
Blessings.......Pastorjim