Just my experience..... The electric wire only works for certain goats. Mostly the bigger ones, and the one that got out and the dogs had him down. He lived to tell about it but decided his side of the fence was a pretty good place to be.
You need woven wire with hot wire around the top, and about a foot up from the bottom. That will keep them in.

I agree with cheribelle, I took my goats to a friend's house to get bred before I got my billy. They were a nubian and a boer, so pretty good sized goats, 150 lbs each I would say. They figured out how to get between the wires with minimal shocking and that meant every single day, sometimes two or three times a day we would have to go and help get them back in, after spending three hours one day, we decided it was time, whether bred or not to bring them home, Our friend's goats never got out, but mine did.
I have on one area, the 4x2" opening fence with barbed wire on the top and bottom, they have never gotten out of this one, and on the other I have the field fencing that has 6x6" on the top and the 6x2" on the bottom,they step up on this fencing and it buckles down, allowing them to jump over. I would not suggest getting the latter fence due to the fact that the goats are CONSTANTLY getting their head stuck in the spaces in the fence! I am always having to get one particular goat unstuck, her horns are just short enough to get through, but just long enough not to get back through.
I can honestly tell my hubby "I told you so" on this one.
Good luck