I have considered goats and my research has revealed a downside, goats will eat any plant they can reach. They can climb fences and as Kennyv points out, they fertilize. So if you have dogs like I do they will roll in the goat waste as any dog will tell you "it smells to good to resist". Male goats or buck as they are referred to, can become a problem, as they are randy (google it). this condition can produced a terrific odor and a nasty disposition.
All this of course can vary depending on which variety of goat you have, but your best bet is a small one of the female gender, one that is edible in case things don't work out, you have a barbecue scenario