Run it on the outside of the fence, a few inches up from the ground, and a few inches out from the fence. Deters most critters that would try to dig under or climb up from the ground. The fence wire is cheap, since it's just a single strand of smooth wire. The insulators will cost just a bit more, and you can get ones that are extra long so they hold the wire out several inches. A fencer (the electric box) can go for as little as $20. More depending on the length of wire, how often you mow, and if you want fancy stuff like solar power.
I saw some electrified poultry mesh for sale on the back of a magazine not too long ago. It was touted as the ultimate solution for super-effective and super-portable fencing. It might be good, but I think it was just an ad writer in overdrive.