I intend to grow a foliage wall in my bedroom by using English Ivy. For convenience and aesthetics I'd prefer using ropes as support. But will it climb?
English Ivy (hedera helix) climbs by thin roots penetrating whatever it clings to. So if you want to use rope, it would be better to use natural fibre rather than nylon which may be too smooth for it to get any grip. It won't climb by wrapping its stems around the rope or net like bindweed, honeysuckle, etc.
Another issue is that ropes will presumably move around quite a lot (e.g. because of air currents), and ivy naturally clings to relatively stable supports like walls, tree trunks, etc. It may never succeed in attaching itself to something as mobile as a rope.
If your foliage wall is intended to cover an actual wall, the ivy will probably soon be putting roots into the real wall, which is presumably not what you want! Beware that so far as Ivy is concerned even solid rock is "porous" if it's left undisturbed for long enough to get a grip on it. Plaster, dryboard, bricks, concrete, etc, won't be much of a challenge for it.
Ignoring your aesthetic preference, I think either a wood panel (with enough spacing behind it so the ivy roots can't penetrate through the wood and into whatever is behind it) or a free-standing wood structure like a pole, tepee, etc, would work better than rope.
I don't think it matters what material you use to train them, but what type of structure you provide for the plants to climb up. To create a foliage "wall" you'd be better off providing a net, in order for the ivy to spread out. Hanging ropes will lead to the thick "green lines" growing around individual ropes.