They do better with browsings, BUT if you can cut/scythe fresh grass in the summer (from the overgrown areas, so nice and long, can contain thistles/nettles/docs etc, but not much in the way of creeping buttercup) then that will go a Long way to satisfy them, especially on wet days/evenings.
Willow will grow quickly if you get some cutings in this coming winter.
Mine have so far respected the electric topwire on the fences (3ft standard sheep netting plus 1 strand of top wire, mains electric powered). Kids learn fast, a few screams and then they are fine.
Depends also where you get your goats from - a goat that knows about jumping will always try and do it, but the seller will seldom mention the reason for selling them is.....