On varmints - harmful and beneficial

Well, they are all varmints. Even the good ones. They are your problem, in your locale.

Here's mine.

The lineup up for good ones are:
chickens
domesticated rabbits
cats

Bad:
groundhog
opposum
racoon
feral cats
rabbits

The chickens free range only at the end of the growing season when summer crops are done and the others are under hoops or, like spinach, are seeded and fenced in. We keep 6 good prime egg layers (currently 1 year old Rhode Island Red). The rest of the time I have a mobile chicken coop (bigger than a chicken tractor, but still a full size coop). I is a 4x6 platform that slides on waxed up 4x4's. I move it down a fence row weekly. I dump lots of leave along the base of the fence to attract worms and crickets (and gardener snake just popped out of one yesterday). When a new run is erected, the chickens just dive into those leaf piles. Chicken heaven! But chickens can escape so you need to fence in the gardens. Which segues into groundhogs.

Fencing all gardens gives you a head start in case a ground hog moves into the area. You'll see them munching grass outside the fence for about one week before they decide to invade the garden. So have the have-a-heart trapped baited with strawberries in the place you saw them last. If birds steal the strawberries, put a piece of bird netting over the opening. It will stop the birds but not the groundhog.

I've had rabbits in hutches but I don't think the small amount of manure is worse the time, the feeding, and dealing with any offspring. I imagine for meat it might be worth it but we are mostly vegetarian here.

And finally cats - fairly useful for the rodent population but certainly not 100% effective. I would say 25% effective. You would have to have 4 or 5. Keep them pretty hungry, and have good "mouser's". But our 2 cats could not be counted on to keep the mice at bay. So every Spring when I would get out the mower or tiller I would see mice come out of the engines where they had built nests. Mouse traps were a little effective - snapping a mouse once a week. But the only deterrent was moth balls. Cover your equipment in a trash bag, and toss a handful of mothballs inside.

Dog's aren't on my list. But if you had a breed that does a job for you, great; like the kind that watch over sheep. Other than maybe barking at invading deer, I don't see any value added (other than companionship). I think getting your fencing deer proof standard should solve that. And lately I even augment it by parking my car near the garden facing the fields with the window slightly down and the car radio tuned to a talk show. Then I put my smelly T shirt from working in the garden looped over the mirror. Ha! If that doesn't deter them then I might as well sit out there with a TV and deer rifle because they'll just walk up to you.

'Possum and feral cats I trap all the time and drop off at the ASPCA. I used to catch a lot of skunks (you cover the trap with a tarp so they don't feel alarms and squirt). But not anymore. Maybe the local fox population got them like they do any Canada geese that think they can breed in the open corn fields. Feral cats come down the block from the feed mill where they like them to hunt the rats and mice. But they carry disease and fight with my cats which are kept outdoors. So I trap them and the ASPCA will determine if the carry a disease which mean end of life right there. Otherwise they try to have the adopted (ha! these things are thick-boned and will pounce at you!).

The raccoons and fox can decimate you chickens as can the hawks. Raccoons are imaginative and persistent. So the coop must be secured at night. Fox are opportunists. We left the coop door open one night and the fox stole 9 out of 11 chickens. It killed and stashed the rest. There were new piles of feathers every morning in different places on the property. I tried a trap but he/she would not go for it. So we just a more careful with the coop.

I do like ducks but they are so low on the food chain! Wandering dogs, raccoons, fox, etc. It just seems like a waste of money and affection ;-)

We've had goats, when the kids were young and drinking milk. I remember trying to keep up the consumption with production and making many goat milkshakes for the kids. But we don't use much milk so it's not worth the time to milk and care for them. And they are excellent escape artists where normal fences mean nothing. And electrical fences give the pleasure in pain. And chaining them in makes them sitting targets for roaming dogs especially when the roam in packs. We've experience that horror too.

The previous owner of my property had sheep - and just for the purpose of clipping the lawn - he was a veterinarian. I suppose some my like them. Again, time is required for feeding and managing the grazing areas. Since I am not doing anything of it as a business I can't see putting the time into it. I'm not running a petting zoo here!