The type of fencing you use depends on the breed of goat. Some of your field fencing types will not work for those that are breeding mini breeds since the kids can slip right on through.
A fence that is around 4 to 5 feet high is recommended. Be sure to use sturdy posts since goats like to climb on the fence, especially if they see you coming with treats.
I use welded wire fencing that has 2x4 holes.
If you deal with predators (wild or domestic) run a strand of electric wire along the top of the fence line.