What gauge is the wire? Deer fencing tends to be somewhat flimsy as they aren't worried about deer pushing on it, only leaping it. And if it's really heavy gauge, I would expect it to be extremely costly. And, of course, "non-rust" doesn't apply to us here in South Texas, home of humidity… I agree with Pat that solid wood is the best choice, though you need a level yard so they can't go under at least easily. And hot wires are a good deterrent for climbers.
That being said, we have 5 foot chain link and none of ours have even tried to climb it, even when deer and squirrels are taunting them. But...they are never out unsupervised for long, except for the 13 year old, who wouldn't dream of climbing...
Terry