"hog panels" are one option that you could use.
they are typically ~4gauge wire and have openings that get smaller as it gets closer to the bottom. like this:
these arent cheap if you are buying new. in my area that are ~$25 per 16 ft piece. depending on how much you're trying to fence in. i have seen used versions for sale in varying conditions for much cheaper though.
this would keep pigs in, not sure about goats or chickens. you could then add a 12-18 in chicken wire around the bottom to discourage digging under the fence.
the quickest picture i could find that shows how the finished fence would look:
hope this helps.
http://www.cloud9farms.com/ - Southern Colorado - Zone 5 (-19*f) - 5300ft elevation - 12in rainfall plus irrigation rights
Dairy cows, "hair" sheep, Kune Kune pigs, chickens, guineas and turkeys