Sheep will not eat the roughage you said you want to clean up. Goats will. We have been raising them for 15 years and if you give them a reason to stay on the property, they won't leave. Byrd said it all, if water gets through your fence, goats will too. Just be sure they have all they need on your side of the fence and they will stay, i.e., food, clean water and shelter. Go to a local breeder and find some goats that are people friendly. Nothing harder to work with, or around, than a skittish goat. Four or five will work for you and get either all does or all wethers, no bucks. They breed like rabbits.