There are hundreds of cultivars of Hedera helix, 'English' ivy. Just Google for an idea of how many. All will seed if allowed to get to the flowering stage, ie if they have topped their support, but most are less vigorous and less trouble than the original species. You would need to consult local experts to know if they would be a problem where you live. I can't say if some of the other Hederas e.g. colchica or canariensis would be hardy for you. Again someone nearer to you could help. Finally if the fence is old, as you say, ivy might just pull it down through sheer weight or wind resistance.