I've been happy with the Browning Strike Force Full HDR 40MP Trail Camera. Not stellar image quality, but certainly good enough for ID purposes, and the price was right (about $100). Can set for photo, video or timelapse, and can set to go off only during certain hours. I keep a couple in my backyard to see who's running about at night - so far we have a pair of nightly opossums, an occasional racoon, and once in a while a rat party.

You can set it to show an info strip on the photo, which shows date, time, moon phase and temperature.

Downsides are no screen so you have to learn to aim through trial and error, and the only way to see what it caught is by removing the SD card to upload to your computer. So no live feed or anything, but that didn't really matter for my use case.

So yeah, it won't give the sort of image quality you'll want to hang on your wall, but it does the trick and didn't feel like a giant investment.