Sounds a lovely move

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The very first thing you need to check when grazing a garden with any animal is poisonous plants, poisonous to livestock that is. We sold three sheep to a family with a large garden and we checked over the garden as carefully as we could. In spite of that, one of the sheep was soon dead, poisoned by eating a toxic plant - inevitably it was the favourite girl!
The thing about keeping farm livestock as pets is that they still need all the care and money spent on them that they do when kept in larger numbers. So you would have to deal with their feet, their fly prevention, worm prevention, food needs in the winter even if there was enough grass in the summer, you would have to be able to shear sheep, pay vet fees for emergencies and you would need to be able to source an immediate replacement if one died suddenly.
I won't mention guinea pigs because I don't like the poor wee critters, but I do think geese would be a nice very low maintenance, long lived option. They can be a bit noisy depending on breed but they can defend themselves quite well - a goose peck is good and painful, like a mole grip holding on with many lbs of goose hanging on, so foxes don't come back for a second try. They also take themselves off to bed when you tell them to and are far more intelligent than you might expect. You have to heft them to your land or they can just fly off but once settled they will stay. I really love my Shetland Geese. They have blue eyes and when we let them hatch goslings they were the most devoted parents and I'm sure they would happily live in the house if we let them
Of course their big plappy feet will squash your dearly nurtured veggies, but a low fence will keep them out. Ours have a pond but a large dog bath will do for water (they have to be able to wash their heads and they do love to take a bath every day. Another plus point is they don't need to be shorn. So my vote goes to geese.