"The edge" is exactly what goats love. Huge variety that only grows on the edge. They will eventually kill hardwood saplings that are small enough for them to bend over by jumping up on their hind legs and leaning them. They then straddle and walk to the end while munching the leaves off. Cool thing is to see the buck lean them over for the does and kids to eat. They will also take care of any stump regrowth in a few years. Multi-flora rose, brambles, poison ivy, sumac, wild berry bushes and wild fruit trees will be gone quick.
As far as everything in sight, they don't eat much typical pasture grass like fescue. That's actually desirable in many cases and many people run goats with cattle.
As far as breed, they can be dairy or meat. Meat goats eat more because they're bigger. I would stay away from any breed that originated from somewhere arid like South Africa. They have issues and so are high maintenance in temperate climates. For meat goats, Kiko is the low maintenance breed. Also, dairy breeds have been bred by crazy goat ladies to be half pet so they're going to tend to be high maintenance too due to being pampered.