Any type of insulated wire should be fine if of modest length and suspended in the air, as pointed out above that is how it used to be done.
However I have my doubts about the effectiveness of 200 feet of wire in a presumably buried or grounded conduit, due to leakage and capacitance.
If the wire can be run overhead, preferably on insulators, then it should be fine. Most electric fence controllers can handle many hundreds of feet of fence, and the controller wont "know" the difference between an overhead wire, and a longer fence.
As regards grounding, all electric fence controllers require a ground, either from a rod or stake installed for the purpose, or often the fence controller is mounted on a metal post or stake that also forms the ground.
In order that the animals may get a shock there must be a continous path for the current. From the output of the controller, to the metal wires of the fence, via the animal and its hoofs to the earth on which the animal stands, and through the general mass of earth back to the controller via the ground rod.
Due to the high voltage and low current, a relatively high resistance ground is fine and no elaborate grounding means is needed.
remember that animals unused to electric fences may stampede at and through it, despite getting a shock.
In time they learn to avoid it.
BTW, if the animals do get through, do make certain that they are ALL on the right side of the fence when re-erecting it !