The best most inexpensive fox, rabbit, coyote, and beaver trap that I know of is a snare. You can make your own or you can buy them already set up. Buy a copy of Fur-Fish and Game magazine there are many ads in there for trapping supplies and most all of them carry snares and components to make snares. There are also plenty of books about various kinds of trapping. I've used snares alot for beaver trapping and they work great! The thing that I really like about them is that they're inexpensive so if you have someone steal it, it's really not that big of a deal. Loose a leg hold trap and that kinda sucks because they're not cheap