Dogs are inevitable if you are trapping anywhere near populated areas. I try to avoid them as much as possible, but I have a catch pole to release them when I do catch them. The only ones that have given me much trouble are pit bulls, I've caught two, and was able to release both uninjured, but it took a while. Every dog I've caught was on private property where it wasn't supposed to be. A catch pole is the best money you will spend.
Make sure you understand the state regs before you start. I don't trap TN but I've heard they're confusing.
For instruction purposes, Mark June's videos and book are worth every penny. Minnesota trapline products is a great place to deal with. They make MB traps which I use and recommend.
You also need to make certain that your staking/drag setup is sufficient to hold a coyote. You don't want something pulling your stake and running off with the trap. A lot of guys starting underestimate what it takes to hold a coyote.
This how I set my coyote traps up:
Every trap has a JC Conner shock spring, followed by a double stake ring, then either an MB chain stake or drag connected by a split ring or quick link. If I want to use rebar I can remove the quick link and run two rebar stake through the ring at angle. This is versatile and gives a few options, any of which will hold a coyote.