Most game cameras on the market these days will take short videos along with photos. Usually an option in the settings menu. Both for length and quality of video.
Pretty much anything you see on Amazon listed as a trail camera will be pretty good quality. I have bought some of the cheapest from Amazon and they were still good. The key thing with video is that it will drain the battery and fill the memory card faster. Not a problem if you plan to recharge and remove the images/video daily or every few days. More of an issue if you are truly leaving it out on a tree in the woods for weeks at a time.
I see "security cameras" as having some big negatives for the use you are describing. They almost always need external power, they are more costly, and usually are not going to be wireless unless you pay for the higher end models.
Game camera is waterproof, battery operated, easy to attach to poles, trees, etc...
