I would come at it from the coop/ enclosure angle. The dog thing is a toss up. You might just end up with one more animal that wants to eat your chickens. Dog to dog that drive can be variable and unpredictably strong. I would be very picky if I were in a position to choose a dog specifically to protect my other animals. Namely wanting to know intimately the natures and histories of the parent dogs. Ideally I would want a puppy out of a dog that was already farm friendly.
My boy so long as he doesn't have direct access to the chickens - so long as they don't fly a fence and land in his yard hasn't had any chicken KILLING incidents and he doesn't have a taste for chickens, and in the past when they have gotten in the wrong space he'll corner them and he'll bruise them, their movement freaks him out and he's squeamish, so they make it home bruised and freaked out, but alive.
He's more of an alarm system than a guard. Unless he's really kicking up a fuss - and sometimes he does, sometimes he doesn't, the chances of me getting out of bed because he's barking (same intensity for a squirrel a a coyote - and hawks... he's useless) are low. I've been desensitized by his habit of barking at anything that moves in the yard at night. Be it leaf or frog or squirrel. He's there to persuade large predators that we're too much trouble to get any closer. Which I suppose is the most a dog can do. The dog that will kill a fox will also kill something else that moves. Actually, I don't think my dog could catch a fox. He's not the type to pick a fight if he isn't sure he can win it, and he doesn't see them as food, so they're just invaders.
Rabbits on the other hand he's passionate about. He got SIGHT of them through a fence and we had to completely redo the fence line to get it dig proof on the side it butts up to the yard.
He's never tasted them either, but just the sight was enough to drive him mindlessly bonkers for about two months till he forgot about them. Meantime, I had to dig, frame and stake the fences on the bottom and bring in fill dirt on the other side to another foot deep. About three days of work. Hecka lot of work, done to preserve the friendship.
Our female dog (a rescue) cannot be trusted period. She'd killed smaller mammals before we got her (gee thanks for not telling us till after the fact rehoming person) and even the goats aren't safe around her. There is no degree of training that will help that. She is the doggy version of an animal serial killer, long ingrained before we got her. Because we can keep her alive, whereas someone with less property couldn't, we do. She's doing life on dog food.
Dogs are a whole nother set of headaches.