Goats.
Make sure your fencing is good - stock fencing with single strand of electric along top and half way up is ideal we find.
If you want essentially pets then I would suggest a pair of castrated males.
Goats can be noisy but generally only when they think it is feeding time - I cant see how a pair of goats will be a noise nuisance
Trees will need protecting as goats will eat the bark.
Goats will not generally eat the grass that close - they are browsers not grazers.
Size / breed depends on a lot of things - how much area? What is available - what do you want to spend? Do you mind horns. Bagots, Boers, Golden Guernseys are my preferences. Angoras are nice but need 2 x yearly shearing
Goats will need a shelter all year round also hay and mineral lick. If just pets doubt they will need much / if any hard feed - depends on quality of grazing / hay / weather etc
Very similar routine husbandry requirements as sheep but advise go on a goat care course first
No don't need locking up at night - can live with chickens as long as cant access the chicken food and the ground is large enough not to be contaminated with chicken poop.
Buttercups Goat Sanctuary look out for homes for goats and run care courses - might be an idea - otherwise depending on where you are other courses might be available or friendly goat keepers willing to show you the ropes
http://www.buttercups.org.uk/husbandry-course.htm