I've got to agree with Martin's opinion of homeowners' associations. There's always a Little Hitler in charge, and the rules are insane. I wouldn't live in a place like that.

Chickens are great. My 'girls' are very quiet except after they've laid an egg, then they cackle (odd, to announce the arrival to predators). They will eat practically anything, including roadkill, and they consider maggots a feast. The larger breeds don't fly much, and can usually be contained with short fences, esp if you move short fencing around for them to weed, debug and scratch up specific areas.

Keep in mind what natural feed you already have: if you have a lot of grass, consider a sheep. If you have a lot of brush, think goats.

If you can have a deepish pond or maybe even an above-ground swimming pool, think fish.

Sue