Goats aren't THAT bad at escaping, or wrecking fences. Our one little field is grazed 24 hours a day in the summer (the girls in the daytime and the boys overnight) and aside from tiny kids sometimes wriggling out at the spring of each year, none of them escape. We don't have special fencing either, 4foot high sheep fencing and a bit of wooden rail fencing on the garden side and we have no electric fence or anything else.
That said if they did get out, they like nothing better than eating veggies and roses. But equally they love the weeds too, I pulled out loads of sticky willies this year, and fed them back to the goats (turns it into better compost that way!).
If you do want trimmers, perhaps sheep would be better- I'm thinking of getting a couple of orphan lambs in the spring to put into our "orchard" (posh name for it) because I know they won't bark the fruit trees, but they'll keep the grass down.